CBSEi Class 10 Sequences (AP and GP) CORE

Sn = [2a + (n 1)d]
S50 = [2x1 + (50 1) (2)]
= 25 [2 + 98]
= (25) x (100) = 2500
Refer to geometric pattern given in ―Introduction‖ under (iv). Here 1 + 3 + 5 + ……+ 50
= 2500 = (50) 2
Using this formula, now you can find this sum to n terms and the sum
1+3+5+……….upto n terms = n 2
Example 25: How many terms of the AP : 1, 4, 7, …….. are needed to give the sum 715?
Solution: Here a = 1, d = 4 1 = 3 and Sn = 715.
We have to find n.
Using the formula
we have 715 = n
2
Sn = [2a + (n 1)d],
= n
2
= n
2
or, 3n 2 – n – 1430 = 0
[2x1 + (n 1) 3],
[2 + 3n 3],
[3n 1)],
This is a quadratic equation. Using quadratic formula,
n = =
63