Question

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

Answer 1

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