Question

Write the first five terms of each of the following sequences whose $n$th terms are:$a_n=\frac{n-2}{3}$

Answer 1

$a_n=\frac{n-2}{3}...................eq\left(1\right)$

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

$a_1=\frac{1-2}{3}$

$⟹a_1=\frac{-1}{3}$

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

$a_2=\frac{2-2}{3}$

$⟹a_2=\frac{0}{3}$

$⟹a_2=0$

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

$a_3=\frac{3-2}{3}$

$⟹a_3=\frac{1}{3}$

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

$a_4=\frac{4-2}{3}$

$⟹a_4=\frac{2}{3}$

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

$a_5=\frac{5-2}{3}$

$⟹a_5=\frac{3}{3}$

$⟹a_5=1$