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Question

Sum of three consecutive terms of an AP is 24 and product is 312. Find the middle term and common diffeerence of the AP.

A
8 and ±5
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B
8 and ±3
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C
6 and ±5
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D
6 and ±3
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Solution

The correct option is A 8 and ±5
Let the given terms be (ad),a and (a+d), where d is common difference.

Given sum of terms = 24

(ad)+a+(a+d)=24

3a=24a=8

So the terms are (8d),8 and (8+d).

Given product of terms = 312.

(8d)×8×(8+d)=312

(8d)(8+d)×8=312

82d2=3128=39

64d2=39

d2=25

d=±5

So, the middle term of the AP is 8 and common difference is ±5.





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