If the sum and product of the first three ter | vedclass

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Question

Let the three number in $A.P.$ are $a-d,a,a+d$

Given that $a-d+a+a+d=33$

$ \Rightarrow a = 11$ and $\left( {a - d} \right)\left( a \right)\

Vedclass · Accepted Answer

$-25$

Vedclass · Answer

Let the three number in $A.P.$ are $a-d,a,a+d$

Given that $a-d+a+a+d=33$

$ \Rightarrow a = 11$ and $\left( {a - d} \right)\left( a \right)\left( {a + d} \right) = 1155$

$ \Rightarrow a\left( {{a^2}{d^2}} \right) = 1155$

$ \Rightarrow 11\left( {121 - {d^2}} \right) = 1155$

$ \Rightarrow {d^2} = 16$

$ \Rightarrow d \pm 4$

If $d=4$ then first term $a-d=7$

If $d=-4$ then first term $a-d=15$

${T_{11}} = 7 + 10 + \left( 4 \right) = 74\,\,\,\,\,{T_{11}} = 15 + 10\left( { - 4} \right) =  - 25$

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

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