a) The first term = 4
b) The common difference = 6
The sum of the first four terms of a linear sequence is 26 and that of the next four terms is 74. Find the values of:a) the first term b) the common difference
2 answers
Starting from scratch, assuming that the AI will be wrong again ....
sum(4) = (4/2)(2a + 3d) = 26
2a + 3d = 13
sum(8) = 26+74 = 100
(8/2)(2a + 7d) = 100
2a + 7d = 25
subtract:
4d = 12
d = 3
backsub in 2a+3d=13
2a + 9 = 13
a = 2
check:
my terms are: 2, 5, 8, 11, 14, 17, 20, 23, 26, ....
the sum of the first 4 is 26, the sum of the next 4 is 74
sum(4) = (4/2)(2a + 3d) = 26
2a + 3d = 13
sum(8) = 26+74 = 100
(8/2)(2a + 7d) = 100
2a + 7d = 25
subtract:
4d = 12
d = 3
backsub in 2a+3d=13
2a + 9 = 13
a = 2
check:
my terms are: 2, 5, 8, 11, 14, 17, 20, 23, 26, ....
the sum of the first 4 is 26, the sum of the next 4 is 74
4 answers