Q26 of 102 Page 410

If the sum of n terms of an AP is , where P and Q are constants then find the common difference.

Let the first term be a and common difference be d


To Find: d


Given: Sum of n terms of AP =



⇒2a + (n - 1)d = 2P + (n - 1)Q
⇒2(a - P) = (n - 1)(Q - d)
Put n = 1 to get the first term as sum of 1 term of an AP is the term itself.


⇒P = a
⇒ (n - 1)(Q - d) = 0
For n not equal to 1 Q = d


Common difference is Q.


More from this chapter

All 102 →
24

If the sum of n terms of an AP is (3n2 + 5n) and its mth term is 164, find the value of m.

 25

Find the sum of all natural numbers from 1 and 100 which are divisible by 4 or 5.

 27

If Sm = m2p and Sn = n2p, where m ≠ n in an AP then prove that Sp = p3.

 28

A carpenter was hired to build 192 window frames. The first day he made 5 frames and each day, thereafter he made 2 more frames than he made the day before. How many days did he take to finish the job?