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The second term of an infinite geometric progression is 2 and its sum to infinity is 8 . The first term is

Correct answer

4

Step-by-step solution

Second term is 2 ⇒ a r = 2 Sum to infinity is 8 ⇒ a 1 - r = 8 Eliminating a we get, 2 / r 1 - r = 8 ⇒ r 1 - r 8 = 2 ⇒ 8 r - 8 r 2 = 2 ⇒ 4 r 2 - 4 r + 1 = 0 ⇒ r = 1 2 ⇒ a = 2 1 2 = 4 .

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