Free Printable 3.1 Sequences and Series

1.

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

a)

70

b)

71

c)

-71

d)

-70

2.

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

a)

-70

b)

-73

c)

70

d)

73

3.

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

a)

-58/15

b)

-50/15

c)

58/15

d)

50/15

4.

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

a)

-27

b)

27

c)

-20

d)

20

5.

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

a)

-1080

b)

-1800

c)

1800

d)

1080

6.

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

a)

1591

b)

-1591

c)

-1590

d)

1590

7.

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

a)

-84

b)

84

c)

-84.05

d)

84.05

8.

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.

a)

878

b)

-878

c)

787

d)

-787

9.

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

a)

10m-9n

b)

-10m-9n

c)

10m+9n

d)

-10m+9n

10.

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

a)

78

b)

-78

c)

-70

d)

70

11.

Find the 10th term of the geometric sequences $\frac{1}{2},1,2,4,...$

a)

-256

b)

256

c)

265

d)

-265

12.

Find the 8th term of the geometric progression -16, 8, -4, 2,...

a)

-1/18

b)

-1/8

c)

1/8

d)

1/18

13.

Find the 9th term of the geometric sequences 0.1, 0.01, 0.001,...

a)

$1\times10^{-9}$

b)

$-1\times10^{-9}$

c)

$1\times10^9$

d)

$-1\times10^9$

14.

Find the sum of the first 8 terms of geometric progressions 3, 6, 12, 24,...

a)

765

b)

-765

c)

756

d)

-756

15.

Find the sum of the first 20 terms of geometric progressions 81, 27, 9, 3,...

a)

120.5

b)

121.5

c)

-120.5

d)

-121.5

16.

Find the sum of the first 10 terms of geometric sequences -240, 48, -9.6, 1.92,...

a)

-100

b)

100

c)

200

d)

-200

17.

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.

a)

$T_5=-72;\ S_{\infty}=910.22$

b)

$T_5=72;\ S_{\infty}=910.22$

c)

$T_5=72;\ S_{\infty}=-910.22$

d)

$T_5=-72;\ S_{\infty}=-910.22$

18.

For what values of x does the sequence

$3,\ 6x,\ 12x^2,...$ have a sum to infinity? ()Hin

a)

$-\frac{1}{2}<x<\frac{1}{2}$

b)

$-\frac{1}{2}>x>\frac{1}{2}$

c)

$-1<x<1$

d)

$-1>x>1$

19.

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

a)

$T_5=\frac{8}{80}$

b)

$T_5=\frac{8}{81}$

c)

$T_5=-\frac{8}{81}$

d)

$T_5=-\frac{8}{80}$

20.

The first three terms of a geometric sequence are $\sqrt{2},2,\sqrt{8}$ . Find the common ratio, r, and the sixth term of the sequence.

a)

$r=-\sqrt{2};\ T_6=8$

b)

$r=\sqrt{2};\ T_6=-8$

c)

$r=\sqrt{2};\ T_6=8$

d)

$r=-\sqrt{2};\ T_6=-8$

3.1 Sequences and Series

Total questions: 20

Worksheet time: 3hrs 11mins

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