Question

Find the ${10}^{th}$ and the ${25}^{th}$ term of the arithmetic progression $7,13,19,25,...$

Answer 1

The given arithmetic progression is $7,13,19,25,...$ Here the first term is $7$ and the common difference is $6$. Thus using the formula $t_n=a+(n-1)d$ to find the ${10}^{th}$ and the ${25}^{th}$ terms, we get,

$t_{10}=7+(10-1)6$

$t_{10}=7+54$

$t_{10}=61$

$t_{25}=7+(25-1)6$

$t_{25}=7+144$

$t_{25}=151$

Solving the equations $1$ and $2$, we get

$t_{10}=61and{t}_{25}=151$

Thus, the ${10}^{th}$ and the ${25}^{th}$ term of the arithmetic progression $7,13,19,25,...$ are $61$ and $151$ respectively.