Asked by Samuel

The third term of a linear sequence is 20 and the sum of the first the first ten terms is 275
Find
The first term and the common differences
The. 37th term of progressing

Answers

Answered by R_scott
3 f + 2 d = 20

10 f + 45 d = 275

solve for f (1st term) and d (common difference)
Answered by mathhelper
The third term of a linear sequence is 20
---> a + 2d = 20 or a = 20-2d
the sum of the first the first ten terms is 275
---> (10/2)(2a + 9d) = 275
10a + 45d = 275
2a + 9d = 55

use substitution:
2(20-2d) + 9d = 55
40 - 4d + 9d = 55
5d = 15
d = 3
then a = 20-6 = 14

the sequence is 14, 17, 20, 23
term(37) = a + 36d = 14 + 108 = 122
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