# AP calculus

The sixth term of an Arithmetic Progression is 23 and the sum of the six terms is 78. Find the first term and the common difference.

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1. a+5d = 23
6/2 * [a + (a+5d)] = 78

a + 5d = 23
6a + 15d = 78

a=3
d=4

sequence: 3 7 11 15 19 23
sum: 78

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2. Given an arithmetic progression -7,-3,1,..., state three consecutive terms in this progression which sum up to 75.

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3. The kth term is a+(k-1)d
so you want

3a + (k-1 + k + k+1)d = 75

3(-7) + 3k(4) = 75
12k = 96
k=8

So, the 8th,9th,10th terms are

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4. I can already tell that's gonna be super hlepufl.

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