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 Mar, 2013, 12:08: AM

Expert Answer:

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  | 9th Mar, 2013, 12:48: AM

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