Question

In an AP, the $9th$ term is $-72$. The $10th$ term is $60$ less than the $4th$ term. Find the first term of the AP

• A. $8$
• B. $-8$
• C. $-152$
• D. $10$

Answer 1

The correct option is A $8$

Given that:

$a_9=-72$ and $a_{10}=a_4-60$

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

$a+8d=-72$ ......(1)

And

$a+9d=a+3d-60$

$\Rightarrow 6d=-60\Rightarrow d=-10.$

Substituting this value in equation (1), we get

$a+8\times (-10)=-72$

$a=80-72$

$a=8$

Hence,

The first term is $8.$