Question

In AP the sum of the fourth term is 10 the product of first term first term and fourth term is 10 times the product of second and third term find the number​

Answer 1

Let the four terms of an A.P. be a-d,a,a+d,a+2d.

According to the first given condition

(a-d)+a+(a+d)+(a+2d)=10

4a+2d=10

.......(÷by2)

2a+d=5

d=-2a+5 ....eq1

According to thesecond given condition

(a-d)×(a+2d)=10×a×(a+d)

{a-(-2a+5)}×{a+2(-2a+5)}=10×a×{a+(-2a+5)}

(a+2a+5)×(a-4a+10)=10a(-a+5)

(3a+5)×(-3a+10)=-10a^2+50a

-9a^2+30a-15a+50=-10a^2+50a

10a^2-9a^2+15a-50a+50=0

a^2-35a+50=0
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