SERIES AND SEQUENCES Flashcards
1
Q
sum of all terms in a sequence
A
series
2
Q
general term of an arithmetic sequence
A
a_n = a + (n - 1) (d)
3
Q
general term of a geometric sequence
A
a_n = a(r)^(n-1)
4
Q
sum of terms of an arithmetic sequence given a, n and d
A
S_n = n / 2 * [(2)(a) + (n-1)(d)]
5
Q
sum of terms of a geometric sequence
|r| > 1
A
S_n = a (r^n - 1) / r - 1
6
Q
sum of terms of a geometric sequence
|r| < 1
A
S_n = a (1 - r^n) / 1 - r
7
Q
sum of terms of an arithmetic sequence given a, a_n, n and d
A
S_n = (n/2)(a+a_n)
8
Q
Consider sequence:
1, 4, 16, 64, 256, …
Find common ratio + 9th term.
A
r = 4
n_9 = 65536
9
Q
The fourth term in an arithmetic sequence is -20, and the eighth term is -10. What is the hundredth term in the sequence?
A
n_100 = 220
10
Q
sum of an infinite geometric series
A
a / 1 - r
