The sum of the first two terms of a geometric progression is x and sum of the last terms is y. If there are n terms in all, then the common ratio is

Assessment: JAMB UTME - Mathematics - 1989 Subject: General Mathematics

Question 1 Report

\frac{x}{y}

\frac{y}{x}

(

\frac{x}{y}

)

\frac{1}{n - 2}

D) (

\frac{y}{x}

)

\frac{1}{n - 2}

Answer Details

Sum of nth term of a G.P = Sn =

\frac{a r^{n} - 1}{r - 1}

sum of the first two terms =

\frac{a r^{2} - 1}{r - 1}

x = a(r + 1)
sum of the last two terms = Sn - Sn - 2
=

\frac{a r^{n} - 1}{r - 1}

\frac{(a r^{n - 1})}{r - 1}

\frac{a (r^{n} - 1 - r^{n - 2} + 1)}{r - 1}

(r2 - 1)
∴

\frac{a r^{n - 2} (r + 1) (r - 1)}{1}

= arn - 2(r + 1) = y
= a(r + 1)r^n - 2
y = xrn - 2
= yrn - 2

\frac{y}{x}

= r = (

\frac{y}{x}

)

\frac{1}{n - 2}

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