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General Form of an AP

If the sum of...

Question

If the sum of three consecutive terms of an AP is 51 and the product of first and third term is 273 find the third term .

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Solution

Let the three consecutive terms of AP be
a-d, a and a+d
Given
a-d+a+a+d= 51
3a=51
a=17 ...(1)
Also given that
(a-d)(a+d)=273
a²-d²=273
17²-d²=273 (from (1))
289-d²=273
d²=16
d=4
So the third term is a+d= 17+4=21

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