Find the sum of the first 10 terms of the following sequence. Round to the nearest hundredth if necessary. 3, 2, 4/3
To find the sum of the first 10 terms of the sequence, we first need to write out the terms:
3, 2, 4/3, ...
To find the pattern in this sequence, we can observe that each term is related to the previous term by dividing by 3 and then multiplying by 2.
So the next term in the sequence would be:
(4/3) * 2 = 8/3
Continuing this pattern, the second to tenth terms would be:
(8/3) * 2 = 16/3
(16/3) * 2 = 32/3
(32/3) * 2 = 64/3
(64/3) * 2 = 128/3
(128/3) * 2 = 256/3
(256/3) * 2 = 512/3
(512/3) * 2 = 1024/3
(1024/3) * 2 = 2048/3
To find the sum of the first 10 terms, we add all these terms together:
3 + 2 + 4/3 + 8/3 + 16/3 + 32/3 + 64/3 + 128/3 + 256/3 + 512/3 + 1024/3 + 2048/3
= 3837/3
= 1279
Therefore, the sum of the first 10 terms of the sequence is 1279.