Question

The sum of the first two terms of a G.P. is 28,
but the sum of the third and fourth terms is
252. Find the second term of the G.P. if the
seventh term is 5103.​

Answer 1

Step-by-step explanation:

a + ar = 28

ar^2 + ar^3 = 252

a(1+r) = 28

ar^2(1+r) = 252

ar^2(1+r)/a(1+r) = r^2 = 252/28 = 9

r = 3 or -3

a(1-3) = 28 ==> a = -14

a(1+3) = 28 ==> a = 7

So, now we need to know that

ar^6 = 5103

7*3^6 = 5103

Unfortunately, that works whether r is 3 or -3

Using r = -3

7+(-21) = -14

7+21 = 28

So, r=3

7r = 21