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If the sum and product of the first thre...

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

A

25

B

`-36`

C

`-25`

D

`-35`

Text Solution

Verified by Experts

The correct Answer is:
C
Let first three terms of an AP as `a - d, a, a +d`
So, `3a = 33 rArr a = 11` [given sum of three terms = 33 and product of terms = 1155]
`rArr (11 -d) 11(11 +d) = 1155` [given]
`rArr 11^(2) -d^(2) = 105`
`rArr d^(2) = 121 - 105 = 16`
`rArr d = -+ 4`
So the first three terms of the AP are either 7, 11, 15 or 15, 11, 7
So, the 11th term is either `7 + (10 xx 4) = 47`
or `15 + (10 xx (-4)) = - 25`
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