There are 21 terms in an AP. the sum of last three terms is 123 and the sum of three middle term is 69. find the AP
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The required AP is 7,11, 14
Total number of terms in AP = 21. (Given)
Sum of three terms in the middle is 69. (Given)
Sum of last three terms is 123. (Given)
T10 + T11 + T12 = 69
a + 9d + a + 10d + a + 11d = 69
3a + 30d = 69
a + 10d = 23 ----- (1)
T19 + T20 + T21 = 123
a + 18d + a + 19d + a + 20d = 123
3a + 57d = 123
a + 19d = 41 ----- (2)
On solving equation (1) & (2), -
a + 10d = 23
a + 19d = 41
-------------------
-9d = -18
d = 3.
Substituting d = 3 in (1),
a + 10d = 23
a + 10(3) = 23
a + 30 = 23
a = 30 - 23
a = 7.
Therefore, The first term is 7 and Common difference = 3.
The required AP is 7,11, 14 ...
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