Question

Write the first five terms of each of the following sequences whose $n$th terms are:$a_n={(-1)}^n.2^n$

Answer 1

$a_n=(-1{)}^n{.2}^n...................eq(1)$

1) To find the first term of sequence $\left(a_1\right)$ put n=1 in eq(1)

$⟹a_1=(-1{)}^1{.2}^1$

$⟹a_1=-1\times 2$

$⟹a_1=-2$

2) To find the second term of sequence $\left(a_2\right)$ put n=2 in eq(1)

$⟹a_2=(-1{)}^2{.2}^2$

$⟹a_2=(-1\times -1)\times (2\times 2)$

$⟹a_2=\left(1\right)\times \left(4\right)$

$⟹a_2=4$

3) To find the third term of sequence $\left(a_3\right)$ put n=3 in eq(1)

$⟹a_3=(-1{)}^3{.2}^3$

$⟹a_3=(-1\times -1\times -1)\times (2\times 2\times 2)$

$⟹a_3=(-1)\times \left(8\right)$

$⟹a_3=-8$

4) To find the fourth term of sequence $\left(a_4\right)$ put n=4 in eq(1)

$⟹a_4=(-1{)}^4{.2}^4$

$⟹a_4=(-1\times -1\times -1\times -1)\times (2\times 2\times 2\times 2)$

$⟹a_4=\left(1\right)\times \left(16\right)$

$⟹a_4=16$

5) To find the fifth term of sequence $\left(a_5\right)$ put n=5 in eq(1)

$⟹a_5=(-1{)}^5{.2}^4$

$⟹a_5=(-1\times -1\times -1\times -1\times -1)\times (2\times 2\times 2\times 2\times 2)$

$⟹a_5=(-1)\times \left(32\right)$

$⟹a_5=-32$