If the sum and product of the first three terms in an A.P. are 33 and 1155 respectively, then a value of its 11th term is

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If the sum and product of the first three terms in an A.P. are 33 and 1155 respectively, then a value of its 11^th term is

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answer is 47.

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Detailed Solution

Let the three terms of A.P. be a–d, a and a+d sum of terms = 3a
3a = 33 $\Rightarrow$ a = 11
So terms are 11–d, 11 and 11 + d product of terms = 11( 121 –d²) = 1155
$\Rightarrow$ 11( 121 –d²) = 1155 $\Rightarrow$ 121 –d²= 105
$\Rightarrow$ d²= 16 $\Rightarrow$ d = ±4
So terms are 7, 11, 15 or 15, 11, 7
$∴$ t₁₁ = 7 + 10(4) (or) t₁₁ = 15 + 10(-4)
$∴$ t₁₁ = 47 (or) t₁₁ = –25