Question

The sum of first four terms is 40 and the sum of first two terms is 4 of a geometric series whose common
ratio is positive. Find the sum of first eight terms.
Hoi!!✌️​

Answer 1

Answer:

Let the sum of the four terms of the geometric series be a+ar+ar2+ar3 and r>0

Given that a+ar=8 and ar2+ar3=72

Now, ar2+ar3=r2(a+ar)=72

⇒r2(8)=72∴r=±3

Since r>0, we have r=3.

Now, a+ar=8⇒a=2

Thus, the geometric series is 2+6+18+54.

Answer 2

Explanation:

The first four terms would be a, ar, ar^2 and ar^3. That means:

(a + ar + ar^2 + ar^3) = 5 (a + ar)

or

(a + ar) + (ar^2 + ar^3) = 5 (a + ar)

or

a (1 + r) + ar ^2 (1 + r) = 5 a (1 + r)

Divide both sides by a (1 +r) and you have

1 + r^2 = 5

or

r^2 = 4

and since you are looking for a positive series, the common ratio r = 2.

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