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The sum of the first 8 terms of a GP is five times the sum of first 4 terms. Find the common ratio.​

User Himmel
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1 Answer

1 vote

Answer:

1

Explanation:

Sum of nth term of a GP is expressed as;

Sn = a(r^n-1)/r-1

The sum of the first 8 terms of a GP is expressed as;

S8 = a(r^8 - 1)/r-1

The sum of first 4 terms is expressed as;

S4 = a(r^4 - 1)/r-1

If the sum of the first 8 terms of a GP is five times the sum of first 4 terms then

S8 = 5S4

a(r^8 - 1)/r-1 = 5[a(r^4 - 1)/r-1]

r^8 - 1 = 5(r^4 - 1)

r^8 - 1 = 5r^4 - 5

r^8 - 5r^4 = -5+1

r^4(r^4 - 5) = -4

r^4 - 5 = -4

r^4 = -4+5

r^4 = 1

r = 1

Hence the common ratio is 1