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

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

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Solution:

$a - d + a + a + d = 33$ $\Rightarrow $ $a = 11$
$a(a^2 - d^2) = 1155$
$121 - d^2 = 105$
$d^2 = 16 \; \Rightarrow \; d = \pm 4$
If $d = 4$ then Ist term = $7$
If $d = -4$ then Ist term = $15$
$T_{11} = 7 + 40 = 47$