If the sum and product of the first three terms in an A.P. are and , respectively , then a value of its term is :Option 1)Option 2)Option 3)Option 4)

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 :
Option 1)
$-35$
Option 2)
$25$
Option 3)
$-36$
Option 4)
$-25$

Answers (1)

A Aadil Khan

Let the terms be

$\\a-d,a,a+d\\\\\:then\:\:3a=33\\\\\:a=11\\\\\:(11-d)(11+d)d=1155\\\\\:(121-d^{2})a=1155\\\\\:121-d^{2}=105\\\\\\\:d^{2}=16\\\\\:d=\pm 14$

$\therefore term =7,11,15\:\:\:or\:\:\:15,11,7\\\\\:t_{11}=a+10d\\\\\:7+10\times4=47$

$\\t_{11}=15+10(-4)\\\\\:15+(-40)\\\\\:=-25$

answer = 4

Option 1)

$-35$

Option 2)

$25$

Option 3)

$-36$

Option 4)
$-25$

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If the sum and product of the first three terms in an A.P. are and , respectively , then a value of its term is :Option 1)Option 2)Option 3)Option 4)

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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 :
Option 1)
$-35$
Option 2)
$25$
Option 3)
$-36$
Option 4)
$-25$