Question

Write the first five terms of each of the following sequences whose $n$th terms are: $a_n=\frac{3n-2}{5}$

Answer 1

$a_n=\frac{3n-2}{5}...................eq\left(1\right)$

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

$⟹a_1=\frac{3\times 1-2}{5}$

$⟹a_1=\frac{3-2}{5}$

$⟹a_1=\frac{1}{5}$

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

$⟹a_2=\frac{3\times 2-2}{5}$

$⟹a_2=\frac{6-2}{5}$

$⟹a_2=\frac{4}{5}$

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

$⟹a_3=\frac{3\times 3-2}{5}$

$⟹a_3=\frac{9-2}{5}$

$⟹a_3=\frac{7}{5}$

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

$⟹a_4=\frac{3\times 4-2}{5}$

$⟹a_4=\frac{12-2}{5}$

$⟹a_4=\frac{10}{5}$

$⟹a_4=2$

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

$⟹a_5=\frac{3\times 5-2}{5}$

$⟹a_5=\frac{15-2}{5}$

$⟹a_5=\frac{13}{5}$