Question

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

Answer 1

3 f + 2 d = 20

10 f + 45 d = 275

solve for f (1st term) and d (common difference)

Answer 2

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