If the common difference in an arithmetic sequence is 4, and the 20th term is 36, what is the first term?

The sum of an arithmetic sequence can be found using the formula   S = n/2(a + l) where S equals sum, n equals # terms, a equals the first term and l equals last term   we know enough of these to find the missing pieces   S = -15 n = 20 a = 4   -15 = 20/2 (4 + l)  now we only have one unknown   -15 = 10 (4 + l) -15 = 40 + 10l -55 = 10l   l = -5.5   so the last term is -5.5   now we can use anothe formula to find the common difference   l = a + (n-1) d    so the last term equals the first term (a) plus # terms -1 times (d) the common difference   -5.5 = 4 + (20-1) d   -9.5 = 19 d   d = -.5   so your common difference is -.5

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