CAT Quantitative Aptitude Questions | CAT Algebra - Progressions questions

The question is about sum of an Arithmetic Progressions. Second term and eighth term of an AP is given and we need to find out the sum up to 8 terms. With some simple but very powerful ideas, one can cut down on a lot of working when it comes to progressions. For example, anchoring a progression around its middle term can be very useful. CAT Exam tests the idea of progression often in the CAT Quantitative Aptitude section and this could also be tested in DI LR section of the CAT Exam as a part of a puzzle.

Question 11: Second term in an AP is 8 and the 8th term is 2 more than thrice the second term. Find the sum up to 8 terms of this AP.

1. 124
2. 108
3. 96
4. 110

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Progressions: Form the equation and you will be through!

Given, Second term of an AP is 8 => a+d =8, 8th term is 2 more than thrice the second term => a+7d = 2 +3(a+d) = 2+3*8 =26 .
a+d =8 -------------- 1
a+7d = 26 -------------- 2
Solving for d in the two equations, we get d = 3 and a =5.
Sum of n terms in an AP = \\frac{n}{2}\\) * [2a +(n-1)d].
=> Sum upto 8 terms in this AP = \\frac{8}{2}\\) * [2*5 + (8-1)3] => 4*[10+21] = 4*31 = 124.

The question is "Second term in an AP is 8 and the 8th term is 2 more than thrice the second term. Find the sum up to 8 terms of this AP."

Hence the answer is "124"

Choice A is the correct answer.