What is the sum of the first 9 terms of the geometric sequence an=7(−2)^n−1 ?

Answer 1

To find the sum of the first 9 terms of the geometric sequence, we can use the formula for the sum of the first n terms of a geometric sequence:

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

Where:
- S_n is the sum of the first n terms
- a is the first term of the sequence
- r is the common ratio of the sequence

In this case, a = 7 and r = -2, since the sequence is given by a_n = 7 * (-2)^(n-1).

Plugging in the values, we get:

S_9 = 7 * (1 - (-2)^9) / (1 - (-2))

S_9 = 7 * (1 - 512) / 3

S_9 = 7 * (-511) / 3

S_9 = -3587

Therefore, the sum of the first 9 terms of the geometric sequence a_n = 7 * (-2)^(n-1) is -3587.

Answer 2

is that right?

Answer 3

Apologies for the mistake in my previous response. Let's correct the calculation for the sum of the first 9 terms of the given geometric sequence:

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

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

In this case, a = 7 (the first term) and r = -2 (the common ratio).

Plugging in these values and n = 9, we get:

S_9 = 7 * (1 - (-2)^9) / (1 - (-2))
S_9 = 7 * (1 - 512) / (1 + 2)
S_9 = 7 * (-511) / 3
S_9 = -3587

Therefore, the correct sum of the first 9 terms of the geometric sequence a_n = 7 * (-2)^(n-1) is -3587.