Find the sum of the first 8 terms of the following sequence. Round to the nearest hundredth if necessary. 2, -3, 9/2,...
To find the sum of the first 8 terms of the sequence, we first need to determine the pattern of the sequence.
The sequence starts with 2, then -3, then 9/2. The pattern seems to be alternating between adding and subtracting, with each subsequent term being multiplied by -3/2.
So, the sequence can be represented as follows:
2, -3, 9/2, -27/4, ...
To find the sum of the first 8 terms, we can write out the terms:
2, -3, 9/2, -27/4, 81/8, -243/16, 729/32, -2187/64
Now, we can add these terms together:
2 + -3 + 9/2 + -27/4 + 81/8 + -243/16 + 729/32 + -2187/64 = -8745/64
Therefore, the sum of the first 8 terms of the sequence is -8745/64.