# Arithmetic and Geometric Progressions

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## Arithmetic Progression

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

Choice A. 124

## Detailed Solution

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 = ${n \over 2}$ * [2a +(n-1)d].

=> Sum upto 8 terms in this AP = ${8 \over 2}$ * [2*5 + (8-1)3] => 4*[10+21] = 4*31 = 124.

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## More questions from Progressions

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. Reinforce these ideas with these questions.