the sum of the first 7 terms of an A.P. is 63 and that
of its next 7 terms is 161. Find the A.P.
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Step-by-step explanation:
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3, 5, 7 , 9...
Step-by-step explanation:
Using S = (n/2) [2a + (n - 1)d] ,where letters have their usual meaning.
For first 7 terms:
⇒ 63 = (7/2) [2a + (7 - 1)d]
⇒ (63 * 2)/7 = [2a + 6d]
⇒ 18 = 2a + 6d
⇒ 9 = a + 3d ⇒ 9 - 3d = a
For next 7 terms:
⇒ 161 = (7/2) [8th term + 14th term]
⇒ (161 x 2)/7 = [a + 7d + a + 13d]
⇒ 46 = 2a + 20d
⇒ 23 = a + 10d
⇒ 23 = 9 - 3d + 10d [from above]
⇒ 2 = d
thus, a = 9 - 3(2) = 3
∴ AP is a , a + d, a + 2d...
3, 3 + 2, 3 + 2(2)...
3 , 5 , 7 ....
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