Question

The sum of all terms of the arithmetic progression having ten terms except for the first term is $99$ and except for the sixth term $89.$ The third term of the progression if the sum of the first and the fifth term is equal to $10$ is

• A. $15$
• B. $5$
• C. $8$
• D. $10$

Answer 1

The correct option is B $5$

Let the terms of AP be $a,a+d,a+2d..$ so on
Then sum of all the terms except the first term,
$99=9a+45d$
$a+5d=11$
Also given,
Sum of first term and the fifth term = 10
$a+a+4d=10$
$a+2d=5$
Solving the two equations, we get
$a=1,d=2$
Then, third term is,
$a+2d=1+4=5$.