Free Printable Progresii. Inductie

1.

Daca $a_1,a_2,a_3,...,a_n\ \$ este o progresie aritmetica si $a_1=23,a_n=5,\ r=-2$ , atunci:

a)

$n=10,\ S_n=140$

b)

$n=20,\ S_n=140$

c)

$n=10,\ S_n=150$

d)

$n=15,\ S_n=150$

e)

$n=10,\ S_n>140$

2.

Daca $a_1,a_2,...,a_n$ este o progresie aritmetica si $a_1=3,\ a_n=39,\ S_n=210$ atunci:

a)

$r=2,\ n=10$

b)

$r=4,\ n=10$

c)

$r=6,\ n=20$

d)

$r=2,\ n>10$

e)

$r=8,\ n\le10$

3.

Daca $a_1,a_2,...,a_n$ este o progresie aritmetica cu $a_1\ge0,\ a_n=18,\ r=2,\ S_n=88$ , atunci:

a)

$a_1=2,\ n=10$

b)

$a_1=6,\ n=20$

c)

$a_1=4,\ n=8$

d)

$a_1=-2,\ n=11$

e)

$a_1>4,\ n=8$

4.

Daca $a_1,a_2,...,a_n$ este o progresie aritmetica cu ratie pozitiva astfel incat $n\ge5,\ a_2+a_4=16,\ a_1\cdot a_5=28$ , atunci:

a)

$a_1=2,\ r=3$

b)

$a_1=4,\ r=1$

c)

$a_1=6,\ r=2$

d)

$a_1>4,\ r=3$

e)

$a_1=14,\ r=-3$

5.

Daca $a_1,a_2,...,a_n$ este o progresie geometrica cu ratie negativa astfel incat $n=9,\ a_1=5,\ a_n=1280$ , atunci:

a)

$S_n=255,\ r=-2$

b)

$S_n=455,\ r=-3$

c)

$S_n=2555,\ r=2$

d)

$S_n=855,\ r=-2$

e)

$S_n>9999,\ r=-1$

6.

Daca $a_1,a_2,...,a_n$ este o progresie geometrica cu toti termenii pozitivi astfel incat $n=3,\ a_3-a_1=136,\ S_n=221$ , atunci:

a)

$a_3=51$

b)

$a_3=150$

c)

$a_3=153$

d)

$a_3>200$

e)

$a_3=215$

7.

Daca $a_1,a_2,...,a_n$ este o progresie geometrica cu toti termenii pozitivi astfel incat $n=7,\ a_1+a_2+a_3=26,\ a_5+a_6+a_7=2106$ , atunci:

a)

$a_7=5108$

b)

$a_7=1506$

c)

$a_7=1530$

d)

$a_7=1458$

e)

$a_7=2154$

8.

Termenul general al sirului $\frac{2}{1\cdot3},\frac{4}{3\cdot5},\frac{6}{5\cdot7},\frac{8}{7\cdot9},...$ definit pentru $n\ge1$ este:

a)

$\frac{2^n}{4n^2-1}$

b)

$\frac{2n}{4n^2-1}$

c)

$\frac{2n}{\left(4n-3\right)\left(4n-1\right)}$

d)

$\frac{2\left(n+1\right)}{4n^2-1}$

e)

$\frac{2n}{n\left(n+2\right)}$

9.

Termenul general al sirului $0,-\frac{1}{9},\frac{4}{16},-\frac{9}{25},\frac{16}{36},...$ definit pentru $n\ge1$ este

a)

$\left(-1\right)^n\ \frac{\left(n-1\right)^2}{\left(n+1\right)^2}$

b)

$\left(-1\right)^{n-1}\ \frac{n^2}{\left(n+2\right)^2}$

c)

$\left(-1\right)^{n-1}\ \frac{\left(n+1\right)^2}{\left(n+2\right)^2}$

d)

$\left(-1\right)^{n-1}\ \frac{n^2}{\left(n+2\right)^2}$

e)

$\left(-1\right)^{n-1}\ \frac{\left(n-1\right)^2}{\left(n+1\right)^2}$

10.

Termenul general al sirului $2,\frac{5}{2},\frac{10}{3},\frac{17}{4},\frac{26}{5},....$ definit pentru $n\ge1$ este

a)

$\frac{\left(n-1\right)^2}{\left(n+1\right)^2}$

b)

$\frac{n^2}{n+1}$

c)

$\frac{n^2-1}{n}$

d)

$\frac{n^2+1}{n}$

e)

$\frac{\left(n+1\right)^2+1}{n+1}$

11.

Fie $S_n=1\cdot3+2\cdot5+3\cdot7+...+n\cdot\left(2n+1\right),\forall n\in N$ Atunci:

a)

$S_n=\frac{1}{36}\left(5n^4-6n^3+109n^2\right)$

b)

$S_n=10n-7$

c)

$S_n=\frac{1}{2}\left(11n^2-13n+8\right)$

d)

$S_n=\frac{1}{6}\left(4n^3+9n^2+5n\right)$

e)

$S_n=n\left(n+1\right)^3$

12.

Fie $S_n=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{n\left(n+1\right)\left(n+2\right)}$ Atunci:

a)

$S_n=\frac{1}{4}-\frac{1}{n\left(n+1\right)\left(n+2\right)}$

b)

$S_n=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{\left(n+1\right)\left(n+2\right)}\right)$

c)

$S_n=\frac{n+1}{n\left(n+1\right)}$

d)

$S_n=\frac{1}{n\left(n+1\right)\left(n+2\right)\left(n+3\right)}$

e)

Formulele precedente sunt toate false

Progresii. Inductie

Total questions: 12

Worksheet time: 1hrs 10mins

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