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CBSE Class 10 Answered

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 | 09 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 | 09 Mar, 2013, 12:48: AM
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