The first term of an arithmetic progression is 1 and the sum of the first nine terms is 369. The first and the ninth term of a geometric progression coincide with the first and the ninth term of the arithmetic progression. The value of seventh term of the geometric progression is ________.

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answer is 27.

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Detailed Solution

369=92[2+(9−1)d]⇒ 82=2+8d⇒ d=10Now, ar8 = a + 8d⇒ 1×r8=1+8×10⇒ r8=81⇒ r=3⇒ ar(7−1)=1×(3)6=27

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