The sum of the 20 terms of an arithmetic sequence is 160. If the last term is -30, what is the first term?
SUM = (F + L) / 2 * N, where F=First term, L=Last term, N=Number of terms.
160 = (F - 30) / 2 * 20, solve for F
160 = 10 (F - 30)
160 = 10 (F - 30) is equivalent to 10 (F - 30) = 160:
10 (F - 30) = 160
10F - 300 = 160
10F = 160 + 300
10F = 460 divide both sides by 10
F = 460 / 10
F = 46 - First term.
SUM = (F + L) / 2 * N, where F=First term, L=Last term, N=Number of terms.
160 = (F - 30) / 2 * 20, solve for F
160 = 10 (F - 30)
160 = 10 (F - 30) is equivalent to 10 (F - 30) = 160:
10 (F - 30) = 160
10F - 300 = 160
10F = 160 + 300
10F = 460 divide both sides by 10
F = 460 / 10
F = 46 - First term.