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  1. In a geometric progression, the sum of the first and the last term is 66 and the product of the second and the last but one term is 128. Determine the first term of the series.
    1. 64
    2. 64 or 2
    3. 2 or 32
    4. 32
Correct Option: B

Let the last term be n, then
Sum of the first and the last term = 66
a + arn – 1 = 66
and ar. arn – 2 = 128
a2rn – 1 = 128
From Eqs. (i) and (ii),
a (66 – a) = 128
⇒ a² – 66a + 128 = 0
⇒ a = 64 , 2



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