This is an arithmetic progression based question from Chapter name- Arithmetic Progression
Chapter number- 9
Exercise – 9.6
In this question we have been given that Sum of the first 14 terms of an A.P. is 1505 and its first term is 10.
Now we have to find its 25th term
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Understanding CBSE Mathematics
Class :- 10th
Question no 34
Given A.P. has first term(a) = 10 and sum of the first 14 terms, S14 = 1505.
By using the formula of the sum of n terms of an A.P.
Sn = n[2a + (n − 1)d] / 2.
=> S14 = 14(2(10) + (14 − 1)d) / 2 = 1505
=> 7(20 + 13d) = 1505
=> 20 + 13d = 215
=> 13d = 195
=> d =15
We know the 25th term is, a25 = 10 + (25 − 1)15
= 10 + 24(15)
= 370
Hence, the 25th term of the A.P is 370