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Find the 10th term of the following sequences: a) 8, 3, -2, -7, ... b) 3, 1, 1/3, 1/9, ...
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2 partsStep-by-step solution
4 steps3) Find the 10th term of the following sequences
Part a· 2 steps
8, 3, -2, -7, ...
Determine the type of sequence.
Calculate the difference between consecutive terms:
Since there is a common difference, , this is an arithmetic sequence. The first term is .Use the formula for the -th term of an arithmetic sequence.
The formula is . We need to find the 10th term, so .
The 10th term is .
Part b
3, 1, , , ...
Determine the type of sequence.
Calculate the ratio between consecutive terms:
Since there is a common ratio, , this is a geometric sequence. The first term is .Use the formula for the -th term of a geometric sequence.
The formula is . We need to find the 10th term, so .
The 10th term is .
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