Question

find the nth term of the series 2/5+13/20+9/10+23/20​

Answer 1

Answer: $\frac{3+5n}{20}$

Step-by-step explanation:

The first term of the series is $\frac{2}{5}$.

Calculate the common difference.

$\frac{13}{20}-\frac{2}{5}=\frac{13-2}{20}=\frac{1}{4}$

$\frac{9}{10}-\frac{13}{20}=\frac{18-13}{20}=\frac{1}{4}$

$\frac{23}{20}-\frac{9}{10}=\frac{23-18}{20}=\frac{1}{4}$

Thus, the common difference is $\frac{1}{4}$.

Calculate the $n^{\rm{th}}$ term of the series.

$\begin{aligned}a_n&=a+(n-1)d\\&=\frac{2}{5}+(n-1)\frac{1}{4}\\&=\frac{2}{5}+\frac{n-1}{4}\\&=\frac{8+5n-5}{20}\\&=\frac{3+5n}{20} \end{aligned}$