CBSEi Class 10 Sequences (AP and GP) CORE

Example 28: The sum of first 22 terms of an AP is 715. If its first term is 1, find the
common difference of the AP.
Solution: Here, a = 1, n = 22 and S22 = 715.
Using the formula.
Sn = [2a + (n 1) d], we have
715 = [2 x 1 + 21d]
or 715 = 11[2 + 21d]
or 2+21d = = 65
or 21d = 65 2 = 63
So, d = = 3
Thus, the required common difference is 3.
Example 29: The sum of first n term of an AP is 3n 2 – 5n. Find its 10 th term.
Solution: Sn = 3n 2 -5n
Note that an = Sn – Sn 1
So, a10 = S10 – S9
= [3(10) 2 – 5x(10)] – [3(9) 2 – 5x(9)]
= [300 – 50] – [243 – 45]
= (250) – (198) = 52
Thus, the required 10 th term is 52.
65