Question

I am COMPLETELY lost on sequences and series stuff. How do you solve the following two:
What is the sum of a 30-term arithmetic sequence where the first term is 74 and the last term is -100?
What is the 22nd term of the arithmetic sequence where a1 = 8 and a9 = 56 ?
Like, how do you plug those into an equation? And what equatino would you use? Just ... gah. Help x_x

Answer 1

For a sequence with 'n' terms, first term 'a' and the last term 'l', the sum 'S' is:
\[S = \frac n 2 (a+l)\]

Answer 2

for the second one, form simple linear equations, to derive 'a' the first term and 'd' the common difference!

Answer 3

Alright, I think I understand the first one. The second one is still a little tricky :/ What do you mean form a simple linear equation?

Answer 4

wat is a1 and a9

Answer 5

For #2


a1 = 8
a9 = a1 + 8d = 56


solve these two equations to find "a1" and "d"!

then, to find any nth term, use the funda-
Tn = a1 + (n-1)d

Answer 6

Alright! Thank you!