The sum of 5th and 9th terms of anap is 72 and sum pf 7th and 12 th terms is 97 find the ap
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Let A be the first term and D be the common difference of AP.
Given, T5 + T9 = 72
(A + 4D) + (A + 8D) = 72
2A + 12D = 72 _____(1)
Given, T7 + T12 = 97
(A + 6D) + (A + 11D) = 97
2A + 17D = 97 _____(2)
(2)-(1),
5D = 25. D = 5
Substituting in (1), A = (72-60)/2 = 6
Thus AP is 6, 11, 16, 21,......
Given, T5 + T9 = 72
(A + 4D) + (A + 8D) = 72
2A + 12D = 72 _____(1)
Given, T7 + T12 = 97
(A + 6D) + (A + 11D) = 97
2A + 17D = 97 _____(2)
(2)-(1),
5D = 25. D = 5
Substituting in (1), A = (72-60)/2 = 6
Thus AP is 6, 11, 16, 21,......
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