Question

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

Answer 1

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

$a_n=3n+2...................eq\left(1\right)$

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

$a_1=3\times 1+2$

$⟹a_1=3+2$

$⟹a_1=5$

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

$a_2=3\times 2+2$

$⟹a_2=6+2$

$⟹a_2=8$

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

$a_3=3\times 3+2$

$⟹a_3=9+2$

$⟹a_3=11$

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

$a_4=3\times 4+2$

$⟹a_4=12+2$

$⟹a_4=14$

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

$a_5=3\times 5+2$

$⟹a_5=15+2$

$⟹a_5=17$