Question

The sum of five consecutive terms in an AP is 80.The product of the first term and the last term is equal to the product of the second term and the third term. State the fifth term. *​

Answer 1

Answer:

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Step-by-step explanation:

so for a certain AP

Let its five terms be (a-2d),(a-d),a,(a+d),

(a+2d) respectively

so according to the first condition

a-2d+a-d+a+a+d+a+2d=80

ie 5a=80

so a=16 (1)

according to the second condition

(a-2d)(a+2d)=(a-d).a

a²-4d²=a²-ad

-4d²=-ad

ie ad=4d²

so thus then

16d=4d² from (1)

4d=d²

ie d²-4d=0

d(d-4)=0

ie d=0 OR d=4

but as common difference between any terms of certain AP can't be zero as A.P is a series containing continuous terms ie common difference between its each and every preceding and succeeding terms is constant,

d=0 is absurd

thus then

d=4

so our fifth term is (a+2d)

=[16+(2×4)]

=16+8

=24

hence the fifth term is 24