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