Question

Write the first five terms of each of the following sequences whose $n$th terms are:$a_n=\frac{2n-3}{6}$

Answer 1

$a_n=\frac{2n-3}{6}...................eq\left(1\right)$

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

$⟹a_1=\frac{2\times 1-3}{6}$

$⟹a_1=\frac{2-3}{6}$

$⟹a_1=-\frac{1}{6}$

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

$⟹a_2=\frac{2\times 2-3}{6}$

$⟹a_2=\frac{4-3}{6}$

$⟹a_2=\frac{1}{6}$

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

$⟹a_3=\frac{2\times 3-3}{6}$

$⟹a_3=\frac{6-3}{6}$

$⟹a_3=\frac{3}{6}$

$⟹a_3=\frac{1}{2}$

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

$⟹a_4=\frac{2\times 4-3}{6}$

$⟹a_4=\frac{8-3}{6}$

$⟹a_4=\frac{5}{6}$

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

$⟹a_5=\frac{2\times 5-3}{6}$

$⟹a_5=\frac{10-3}{6}$

$⟹a_5=\frac{7}{6}$