Question

which term of the A. p 5,15,25,....will be 60 more than its 9th term​

Answer 1

Answer:

15th term of ap will 60 more than its 9th term

Answer 2

$\bf{\Huge{\underline{\boxed{\bf{\red{ANSWER\::}}}}}}$

$\bf{\Large{\underline{\bf{Given\::}}}}$

A.P. is 5,15,25.....will be 60 more than its 9th term.

$\bf{\Large{\underline{\bf{To\:find\::}}}}$

Which term of the A.P.

$\bf{\Large{\underline{\sf{\blue{Explanation\::}}}}}$

Assume the A.P. 5,15,25.....

We know that nth term of an A.P.;

→ an = a+(n-1)d

$\bf{We\:have\begin{cases}\sf{The\:first\:term,[a]=5}\\ \sf{The\:common\:difference[d]=15-5=10}\\ \sf{The\:an = 9}\end{cases}}$

$\longmapsto\sf{a9=5+(9-1)10}$

$\longmapsto\sf{a9=5+(8)10}$

$\longmapsto\sf{a9=5+80}$

$\longmapsto\sf{a9=85}$

According to the question:

an = 60 + a9

$\longmapsto\sf{a+(n-1)d=60+a9}$

$\longmapsto\sf{5+(n-1)10=60+85}$

$\longmapsto\sf{5+(n-1)10=145}$

$\longmapsto\sf{5+10n-10=145}$

$\longmapsto\sf{10n-5=145}$

$\longmapsto\sf{10n=145+5}$

$\longmapsto\sf{10n=150}$

$\longmapsto\sf{n=\cancel{\frac{150}{10} }}$

$\longmapsto\sf{n=15}$

Thus,

The term[n] = 15th term.