Question

Write the first five terms of each of the following sequences whose $n$th terms are:$a_n=3^n$

Answer 1

The $n^{th}$ term of the sequence is

$a_n=3^n...................eq\left(1\right)$

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

$a_1=3^1$

$⟹a_1=3$

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

$a_2=3^2$

$⟹a_2=3\times 3$

$⟹a_2=9$

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

$a_3=3^3$

$⟹a_3=3\times 3\times 3$

$⟹a_3=27$

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

$a_4=3^4$

$⟹a_4=3\times 3\times 3\times 3$

$⟹a_4=81$

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

$a_5=3^5$

$⟹a_5=3\times 3\times 3\times 3\times 3$

$⟹a_5=243$