CBSEi Class 10 Sequences (AP and GP) CORE

So, n = or 22,
Certainly n cannot be .
Thus, n = 22,
i.e., the required number of terms is 22.
Example 26: Find the sum of first 20 terms of the AP: 3, 1, 1, -3,……
Solution: Here a=3, d= 1 3 = 2, n = 20.
Using Sn = [2a + (n 1)d], we get
S20 = [2x3 + (20 1) ( 2)]
= 10 (6 – 38) = 320.
Thus, the sum of first 20 terms of the given AP is 320.
Example 27: The sum of first 25 terms of an AP is 1600. If its common difference is 5,
find the first term.
Solution: Here d=5, n=25 and S25 = 1600
Using Sn = n
2
[2a + (n 1) d], we get
1600 = [2a + (25 1) (5)]
or 1600 = [2a + 120]
or 3200 = 50a + 3000
or a = 4
Thus, first term of the AP is 4.
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