The third term of a geometric progression is 128 and the seventh term is 40.5. Find the fifth term and the sum to infinity.

T 5 = 72 ; S ∞ = 910.22 T_5=72;\ S_{\infty}=910.22 T 5 = 7 2 ; S ∞ = 9 1 0 . 2 2

T 5 = − 72 ; S ∞ = 910.22 T_5=-72;\ S_{\infty}=910.22 T 5 = − 7 2 ; S ∞ = 9 1 0 . 2 2

T 5 = 72 ; S ∞ = − 910.22 T_5=72;\ S_{\infty}=-910.22 T 5 = 7 2 ; S ∞ = − 9 1 0 . 2 2

T 5 = − 72 ; S ∞ = − 910.22 T_5=-72;\ S_{\infty}=-910.22 T 5 = − 7 2 ; S ∞ = − 9 1 0 . 2 2

Find the fifth term of the geometric sequence with a first term of 8 and a sum to infinity of 12.

T 5 = 8 81 T_5=\frac{8}{81} T 5 = 8 1 8

T 5 = 8 80 T_5=\frac{8}{80} T 5 = 8 0 8

T 5 = − 8 81 T_5=-\frac{8}{81} T 5 = − 8 1 8

T 5 = − 8 80 T_5=-\frac{8}{80} T 5 = − 8 0 8

The first three terms of a geometric sequence are 2 , 2 , 8 \sqrt{2},2,\sqrt{8} 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> , 2 , 8 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> . Find the common ratio, r, and the sixth term of the sequence.

r = 2 ; T 6 = 8 r=\sqrt{2};\ T_6=8 r = 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> ; T 6 = 8

r = − 2 ; T 6 = 8 r=-\sqrt{2};\ T_6=8 r = − 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> ; T 6 = 8

r = 2 ; T 6 = − 8 r=\sqrt{2};\ T_6=-8 r = 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> ; T 6 = − 8

r = − 2 ; T 6 = − 8 r=-\sqrt{2};\ T_6=-8 r = − 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> ; T 6 = − 8

3.1 Sequences and Series

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Mathematics

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MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Find the 12th term of the arithmetic sequences 5, 11, 17, 23,..

-71

-70

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.2

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Find the 15th term of the arithmetic sequences -3, -8, -13,..

-70

-73

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.2

CCSS.HSF.IF.A.3

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Find the 7th term of the arithmetic progressions $\frac{2}{3},\frac{6}{5},\frac{26}{15},...$

-58/15

-50/15

58/15

50/15

Tags

CCSS.HSF.BF.A.2

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Find the sum of the first 9 terms of arithmetic progressions 21, 15, 9,...

-27

-20

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.2

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Find the sum of the first 18 terms of arithmetic progressions -8, 0, 8,...

-1080

-1800

1800

1080

Tags

CCSS.HSF.BF.A.2

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Find the sum of the arithmetic progressions 7, 9, 11,...,79. (Hint: find Tn first)

1591

-1591

-1590

1590

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.2

CCSS.HSF.IF.A.3

MULTIPLE CHOICE QUESTION

10 mins • 1 pt

Find the sum of the arithmetic progressions 0.05, 0.15, 0.25, ..., 4.05. (Hint: find Tn first)

-84

-84.05

84.05

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.2

CCSS.HSF.IF.A.3

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3.1 Sequences and Series

Find the 12th term of the arithmetic sequences 5, 11, 17, 23,..

Find the 15th term of the arithmetic sequences -3, -8, -13,..

Find the 7th term of the arithmetic progressions $\frac{2}{3},\frac{6}{5},\frac{26}{15},...$

Find the sum of the first 9 terms of arithmetic progressions 21, 15, 9,...

Find the sum of the first 18 terms of arithmetic progressions -8, 0, 8,...

Find the sum of the arithmetic progressions 7, 9, 11,...,79. (Hint: find Tn first)

Find the sum of the arithmetic progressions 0.05, 0.15, 0.25, ..., 4.05. (Hint: find Tn first)

In an arithmetic sequence, the fifth term is 34 and the tenth term is 43. Find the sum of the first 20 terms of the sequence.

The first three terms of an arithmetic sequence are m, 2m+n, 3m+2n,... Find the tenth term in terms of m and n.

The third term of an arithmetic sequence is 12 and the sum of the first eight terms is 168. Find the 14th term.

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3.1 Sequences and Series

Find the 12th term of the arithmetic sequences 5, 11, 17, 23,..

Find the 15th term of the arithmetic sequences -3, -8, -13,..

Find the 7th term of the arithmetic progressions 23,65,2615,...\frac{2}{3},\frac{6}{5},\frac{26}{15},...32​,56​,1526​,...

Find the sum of the first 9 terms of arithmetic progressions 21, 15, 9,...

Find the sum of the first 18 terms of arithmetic progressions -8, 0, 8,...

Find the sum of the arithmetic progressions 7, 9, 11,...,79. (Hint: find Tn first)

Find the sum of the arithmetic progressions 0.05, 0.15, 0.25, ..., 4.05. (Hint: find Tn first)

In an arithmetic sequence, the fifth term is 34 and the tenth term is 43. Find the sum of the first 20 terms of the sequence.

The first three terms of an arithmetic sequence are m, 2m+n, 3m+2n,... Find the tenth term in terms of m and n.

The third term of an arithmetic sequence is 12 and the sum of the first eight terms is 168. Find the 14th term.

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Discover more resources for Mathematics

Find the 7th term of the arithmetic progressions $\frac{2}{3},\frac{6}{5},\frac{26}{15},...$