Question

The fourth term of G.P is greater than first term, which is positive by 372. The third term is greater than the second by 60. Calculate the common ratio and first term of the progression.​

Answer 1

Answer:

t⁴ = t+372 ar³ = a +372 ...i

t³ = t²+60 ar²= ar +60 ....ii

Explanation:

Let a be the first term and r be the common ratio of the G.P

a=a, a²=ar, a³=ar2, a⁴=ar3

By the given condition,

a³=a+9

⇒ar²=a+9....(1)

a2=a⁴+18

⇒ar=ar³+18....

From (1) and (2), we get

a(r²−1)=9....(3)

ar(1−r²)=18....(4)

Dividing (4) and (3), we get

a(r2−1)ar(1−r2)=918

⇒−r=2

⇒r=−2

Substituting the value of r in (1), we get

4a=a+9

⇒3a=9

∴a=3

⇒a=3

⇒a²=3(−2)=−6

⇒a