Question

The sum of the 1st 4term of a linear sequence AP is 26.And that of the next 4term is 74.Find rhe value of the 1st term and common difference

Answer 1

sum(n) = (n/2)(2a + (n-1)d )

sum(4) = 2(2a + 3d) = 26
2a + 3d = 13

sum(8) = 4(2a + 7d) = 26+74 = 100
2a + 7d = 25

subtract: 4d = 25-13 = 12
d = 3

sub into 2a + 3d = 13
2a + 9 = 13
a = 2

check:

terms are 2, 5, 8, 11, 14, 17, 20, 23
2+5+8+11 = 26
14+17+20+23 = 74

all is good!