Question

The sum of the second and the third terms of a G.P. is 280 and sum of the 5th and 6th term is 4375. Find the 4th term of G.P.​

Answer 1

Answer: 32 is the first term find accordingly

Answer 2

Answer:

4th term =500

Step-by-step explanation:

Let the first term be a and common ratio be r.

So,2nd term =ar and 3rd term =ar²

A/q, ar+ar²=280

=> ar(1+r)=280 ---------(1)

Similarly, 5th term =ar⁴ and 6th term =ar⁵

A/q, ar⁴+ar⁵=4375

=>ar⁴(1+r)=4375 --------(2)

Now, dividing eqn (2) by (1) on both sides,

(ar⁴(1+r))/(ar(1+r))=4375/280

=>r³=15.625

=>r=2.5

Substituting r in equation 1,we get

a×2.5(1+2.5)=280

=>2.5a×3.5=280

=>a=280/(2.5×3.5)

=>a=32

Therefore,4th term =ar³=32×2.5³=500

HOPE THIS HELPS .