Monday, April 21, 2014

The sum of the arithmetic is 192 with a last term of 27 and a common difference of 2. Find the number of terms.

Setting up our equations we find:

192=%28n%2F2%29%28a%5B1%5D%2B27%29 and 27=a%5B1%5D%2B%28n-1%29%2A2

Solving the system by substitution leads to two possible solutions, both valid.
a%5B1%5D=5n=12

or
a%5B1%5D=-3n=16

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