Find the sum of the first 9 terms of the following sequence. Round to the nearest hundredth if necessary.
40, comma, minus, 16, comma, start fraction, 32, divided by, 5, end fraction, comma, point, point, .
40,−16,
5
32
,...
To find the sum of the first 9 terms, we first need to write out the sequence:
40, −16, 5, 32/5, ...
Next, we find the common ratio for this sequence. Since the sequence is not geometric, we will find the explicit formula for the sequence:
a_n = 40 + (-16)(-1)^(n-1) for n ≥ 1
Now, we find the sum of the first 9 terms:
S_9 = (40 + (-16) + 5 + 32/5) + (40 + (-16)*(-1)^1 + 5 + 32/5) + ... + (40 + (-16)*(-1)^8 + 5 + 32/5)
S_9 = 9(40) + 9(5) + 9(32/5) = 360 + 45 + 57.6 = 462.6
The sum of the first 9 terms of the sequence is 462.6.