Question

The sum of the $2^{nd}$ and the $7^{th}$ terms of an AP is $30$. If its ${15}^{th}$ term is $1$ less than twice its $8^{th}$ term, find the AP.

Answer 1

Given: $a_2+a_7=30$

Let the first term be a and common difference be $d$.

So, $a+d+a+6d=30$

$2a+7d=30$ --- (1)

${15}^{th}$ term is 1 less than twice the $8^{th}$ term,

So, $a+14d=2(a+7d)–1$

$a+14d=2a+14d–1$

$\Rightarrow a=1$

Substitute the value of $a$ in equation $1$,

$2\times 1+7d=30$

$\Rightarrow d=4$

Therefore, A.P. are $1,5,9,13,.....$