geometric sequence?

Question

Three sums obtained from a particular infinite geometric sequence are S1=10, S2=15 and S3=35/2. The sum of this entire infinite sequence is???

Answer 1

Note that by definition,

S1 = a1
S2 = a1 + a2

So we can actually get these values.

S1 = a1 = 10

This means the first term, a1, is 10.

S2 = a1 + a2 = 15, therefore
a1 + a2 = 15. Since a1 = 10, it follows that
10 + a2 = 15
a2 = 5

So a1 = 10, a2 = 5. We can obtain the ratio now; it's equal to
(a2)/(a1) = 5/10 = 1/2.

r = 1/2

With a1 = 10, r = 1/2, we can now obtain the sum of the infinite series. Note that the sum of an infinite series is determined by the formula

S = a1 / (1 - r)

Plugging in our values,

S = 10 / (1 - (1/2))
S = 10 / (1/2)
S = 20

Answer 2

First take the adjustments, 40 8, 24, 12,... they are not consistent so it extremely is not arithmetic Now see if there's a trouble-free ratio, ninety six/40 8 = 2, 40 8/24 = 2, .... particular so the sequence is geometric.