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
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)
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
---> 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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