Question

the sum of the 1st 3terms if an ap is 33 if the product of the 1st term and 3rd term exceed the 2nd term by 29 find ap and also find the sum of 1st 25 terms ​

Answer 1

Answer:

Let the first three terms of AP is a-d, a, a+da−d,a,a+d.

According to problem,

a-d+a+a+d=33a−d+a+a+d=33 \rightarrow (1)→(1)

(a-d)(a+d)=a+29\rightarrow (2)(a−d)(a+d)=a+29→(2)

From (1)(1), we get

3a=333a=33

a=11a=11

From (2)(2), we get

a^2-d^2=a+29\rightarrow (3)a2−d2=a+29→(3)

Put a=11a=11 in equation (3)(3)

121-d^2=11+29121−d2=11+29

121-d^2=40121−d2=40

121-40=d^2121−40=d2

81=d^281=d2

d=\pm 9d=±9

When a=11a=11 & d=9d=9

A.P: 2,11, 20, 29,.....2,11,20,29,.....

When a=11a=11 & d=-9d=−9

A.P: 20, 11, 2,.....20,11,2,......