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Angelina_Jolie [31]
2 years ago
13

The sum of the second and third terms of G.P is six times the fourth term. Find the two possible values of the common ratio​

Mathematics
1 answer:
andrew-mc [135]2 years ago
8 0

Answer:

Step-by-step explanation:

Let “a” be the first term and ”r” the common ratio of the GP. Then,

f(n) = ar^(n - 1).

f(2) + f(3) = 6f(4). (given)

ar + ar^2 = 6ar^3, or

1 + r = 6r^2, or

6r^2 - r - 1 = 0,

(3r + 1)(2r - 1) = 0.

r = -1/3, or 1/2.

If the common ratio is positive and the second term is 8 we have,

ar = 8, or

a*1/2 = 8, or a = 16.

f(n) = 16*(1/2)^(n - 1) = 2^4*2^(1 - n), or

f(n) = 2^(5 - n).

The first six terms of the GP are : 16, 8, 4, 2, 1, 1/2,…

××××××××××

Checking : f(2) + f(3) = 6f(4), (given).

LHS = 8 + 4 = 12.

RHS = 6* 2 = 12.

LHS = RHS.

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