Question

The second term of a geometric series is 8 and the sum of the first three terms of the series is 42. Find the two possible values of the common ratio of te series

Answer 1

Answer:

r =4 or r=1/4

Step-by-step explanation:

Given:

a2=8

ar=8

a= 8/r -------->(1)

we know that,

$a1 + a2 + a3 = 42 \\ a + ar + a {r}^{2} = 42$

Substituting the value of 'a' from eqn (1)

we get,

$\frac{8}{r} + \frac{8}{r} r + \frac{8}{r} {r}^{2} = 42 \\ \frac{8 + 8 {r}^{2} }{r} = 34 \\ 0 = 8 {r}^{2} - 34r + 8$

Factorising the above equation

we get,

0= 8r^2 - 32r - 2r +8

0= (r - 4)(8r - 2)

Thus, r=4 or r=1/4