If the sum of the first two terms of a G.P. is 3, and the sum of the second and the third terms is -6, find the sum of the first term and the common ratio

Assessment: JAMB UTME - Mathematics - 2013 Subject: General Mathematics

Question 1 Report

-2

-3

-5

Answer Details

Using Sn =

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

we get S2 = 3 =

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

giving 3(r - 1) = a(r2 - 1)
3r - 3 = ar2 - a
ar2 - 3r - a = -3 ..... (1)
ar + ar2 = -6 ..... (2)
From (2), a =

\frac{- 6}{(r + r^{2})}

Substitute

\frac{- 6}{(r + r^{2})}

for a in (1)

(\frac{- 6}{(r + r^{2})}) r^{2} - 3 r - \frac{- 6}{(r + r^{2})} = - 3

Multiply through by (r + r2) to get
-6r2 - 3r(r + r2) + 6 = -3(r + r2)
-6r2 - 3r2 - 3r3 + 6 = -3r - 3r2
Equating to zero, we have
3r3 - 3r2 + 3r2 + 6r2 - 3r - 6 = 0
This reduces to;
3r3 + 6r2 - 3r - 6 = 0
3(r3 + 2r2 - r - 2) = 0
By the factor theorem,
(r + 2): f(-2) = (-2)3 + 2(-2)2 - (-2) - 2
-8 + 8 + 2 - 2 = 0
giving r = -2 as the only valid value of r for the G.P.
From (3), =

\frac{- 6}{- 2 + (- 2)^{2}} = \frac{- 6}{- 2 + 4}

a = -6/2 = -3
Hence (a + r) = (-3 + -2) = -5

Read lesson note on Sequence And Series (WAEC)

Sequence And Series

View Answer

If the sum of the first two terms of a G.P. is 3, and the sum of the second and the third terms is -6, find the sum of the first term and the common ratio

Related Questions

Download The App On Google Playstore