Question

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What is the 32nd term of the arithmetic sequence where a1 = -34 and a9 = -122?
-408
-397
-386
-375

Answer 1

Since we are looking at an arithmetic sequence, each term is the sum of the previous term and sum number (which we will call 'd').
Since a1 = -34 and a9 = -122, you can solve for 'd' (also known as the 'difference') by doing: \[-122 - (-34) = -88\]
\[-88/8 = -11 = d\]
As I mentioned before, 'd' is the 'difference' between each term in the arithmetic sequence. Using the general formula for an arithmetic sequence, aN = a1 + d(N-1) (where 'N' is the number of the term you want in the sequence), you can find the 32nd term.