Find the sum of the first 10 terms of the sequence:

Question

3
,

6
,

12
,

24
,

…

Answer 1

The given sequence is a geometric sequence with the first term (a) = 3 and the common ratio (r) = 2.

The formula for the sum of the first n terms of a geometric sequence is:

S_n = a(1 - r^n) / (1 - r)

Substituting the given values, we get:

S_10 = 3(1 - 2^10) / (1 - 2)

S_10 = 3(1 - 1024) / (-1)

S_10 = -3(1023)

S_10 = -3069

Therefore, the sum of the first 10 terms of the given sequence is -3069.

Answer 2

A geometric series with first term 3 converges to the sum of 2. Find the common ratio of the series

Answer 3

AAAaannndd the bot gets it wrong yet again!

ok until this step:
S_10 = 3(1 - 1024) / (-1)
S_10 = 3(-1023)
S_10 = 3069
it should have been obvious that the sum of positive terms could not be negative!
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3/(1-r) = 2
3/2 = 1-r
r = -1/2