Question

The sum of the first 5 terms of an arthmetic sequence, is 30 and the sum of the next 4 terms is 69 .
Find the arthemetic progression?

Answer 1

so the sum of the first 9 terms would be 99

sum(5) = 30 ---> (5/2)(2a + 4d) = 30
5(2a+4d) = 60
2a + 4d = 12
a + 2d = 6

sum(9) = 99 ----> (9/2)(2a + 8d) = 99
2a + 8d = 22
a + 4d = 11

subtract them
2d = 5
d = 5/2 or 2.5
then a = 1

the arithmetic sequence is
1 , 3.5, 6, 8.5 , ...

Answer 2

What is lhe sum of lhe first 12 terms of an A.p whose first term is 15 and common difference is 13.

Answer 3

1038