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# The sum of the 20 terms of an arithmetic sequence is 160. If the last term is -30, what is the first term?

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The sum of the 20 terms of an arithmetic sequence is 160. If the last term is -30, what is the first term?

Guest Jul 23, 2017

#1
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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.

Guest Jul 23, 2017
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#1
+1

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.

Guest Jul 23, 2017

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