# maths

the sum of the first two terms of a GP is 28,but the sum of the third and fourth terms is 252.find the second term of the gp if the seventh term is 5103. please help.

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1. 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

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2. Thanks for the solution

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4. Thanks for the reasonable solution

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5. Nice one

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6. How can I get the second term of the gp if the seventh term is 5103

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