F.5 Arithmetic sequence urgent

Irene

2013-11-26 12:01 pm

In an arithmetic sequence, the common difference is 8, the last term is 158 and the sum of the terms is 1640. Find the first term and the number of terms.

回答 (1)

七瀨遙

2013-11-26 2:24 pm

✔ 最佳答案

Let a be the first term and n be the number of terms:

158 = a + 8(n -1) ....... (1)
1640 = (n/2)[2a + 8(n-1)] ....... (2)

Arranging terms in (1),
a = 158 - 8(n-1) ....... (3)

By substituting (3) into (2),
1640 = (n/2)[2(158) - 16(n-1) + 8(n-1)]
1640 = (n/2)[316 - 8(n-1)]
1640 = (n/2)[324 - 8n]
1640 = 162n - 4n^2
4n^2 - 162 n + 1640 = 0

By solving the equation, we get n = 20.5 or 20.
Since n is an integral, n = 20.5 is rejected.

Therefore, n, hence the number of terms is 20

By substituting n = 20 into (3),
a = 158 - 8(20-1) = 158 -160 +8 = 6

Therefore, the first term is 6

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