The sum of the first 18 terms of an arithmetic series is 576. The common difference is –8. Determine the value?
The sum of the first 18 terms of an arithmetic series is 576. The common difference is –8. Determine the value of the first term, t1.
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Determine the sum of the arithmetic series 6 + 11 + 16 +A+ 91?
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You have
a + 0*-8 +
a + 1*-8 +
a + 2*-8 +
...
a + 17*-8 = 576
Sum = 18 * a - 8 (0 + 17) * 18 / 2 =
18 a - 1224 = 576
18a = 1800
a = 100 ← ANSWER
(Checked via spreadsheet)
In the second problem, presumably "A" = a bunch of terms ...
Common difference is 5
91 - 6 = 85 / 5 = 17 "gaps", so again 18 terms
Sum is 18 * 6 + (0 + 85) * 9 = 9 * 97 = 873
(Also checked via spreadsheet)