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# an AP has 21 terms. the sum of it's 10th, 11th,12th terms is 129 and the sum of the last three terms is 237. find the AP.

Asked by anukeshd 9th March 2013, 12:08 AM
Answer : Given : an AP has 21 terms. the sum of it's 10th, 11th,12th terms is 129 and the sum of the last three terms is 237
To find : AP

Let a and d be the first term and common difference of the given A.P.
10 + a 11 + a 12 = 129
=> (a + 9d) + (a + 10d) + (a + 11d) = 129 [an = a + (n – 1)d]
=> 3a + 30d = 129
=> a + 10d = 43 … (1)
19 + a 20 + a 21 = 237
=> (a + 18d) + (a + 19d) + (a + 20d) = 237
=> 3a + 57d = 237
=> a + 19d = 79 … (2)
Solving (1) and (2), we get
a + 19d – a – 10d = 79 – 43
=> 9d = 36
=> d = 4
When d = 4, we get
a + 10 * 4 = 43
=> a = 43 – 40 = 3
Thus, the given A.P. is 3, 7, 11, 15… Answer
Answered by Expert 9th March 2013, 12:48 AM
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