Kenneth S. answered • 09/13/16

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Since the sequence is arithmetic (this is an adjective, so it's MET syllable is the one stressed), there's a constant difference from one term to the next. Obviously this means d = 2.5 in this case.

Starting back at the first term, 7, we must take 40 steps to get to the 41st term. Add 40(2.5) = 100, getting the answer 107.

There's a formula for adding up the arithmetic sequence: a + (a+d) +...+[a+(n-1)d] = na + ½n(n-1)d;

in this instance we get S

_{101}= 101(7) + ½(101)(100)(2.5) = 707 + (101)(50)(2.5) = 13332.Check all computations!