Arithmetic n-th Term
This is the value of the common difference, d, for the sequence 1, 5, 9, 13, ...
4
This is the value of the common ratio, r, for the sequence 3, 15, 75, 375, ...
5
The sum of the first 3 terms of the series 5+7+9+...
21
The sum of the first 3 terms of the geometric series 1+2+4+...
7
Find the next three terms in the sequence 2, 8, 32, 128, ...
512, 2048, 8192
This is the next term in the arithmetic sequence 50, 43, 36, 29, ...
22
This is the value of the 5th term (a5) for the sequence 1, 4, 16, 64, ...
256
The sum of the first 8 terms of the series where a1 = 4 and a8 = 32.
144
The sum of the first 4 terms of the series where the first term is 5 and the common ratio is 2.
75
The sequence 3, 7, 11, 15, ... is an arithmetic sequence.
a) What is the common difference (d)
b) Find the 25th term of the sequence.
d = 4, a25 = 99
The value of the 15th term (a15) for the sequence 10, 12, 14, 16, ...
38
The 6th term (a6) of the sequence 1000, 100, 10, 1, ...
0.001 or 1/1000
The sum of the first 10 terms of the arithmetic series 2, 6, 10, 14, ...
200
The sum of the first 5 terms of the geometric series 3, -6, 12, -24, ...
33
The sequence 320, 160, 80, 40, ... is a geometric sequence.
a) What is the common ratio (r)?
b) Find the 9th term of the sequence. Express your answer as a simplified fraction.
r = 1/2, a9 = 1 1/4
The 30th term (a30) of the sequence 20, 13, 6, -1, ...
-183
The 7th term (a7) of the sequence 4, -12, 36, -108, ...
2916
The sum of the first 12 terms of the arithmetic series $15, 12, 9, ...
-54
The sum of the infinite geometric series 10, 5, 2.5, 1.25, ...
20
You are given the arithmetic sequence 100, 95, 90, ..., 15.
a) What is the common difference (d)?
b) Find the number of terms (n) in this sequence.
d = -5, n = 18
The number of terms, n, in the sequence 5, 8, 11, ..., 95.
31
The 10th term (a10) of the sequence 256, 128, 64, ..., expressed as a simplified fraction.
1/2
The sum of the arithmetic series 3+8+13+...+93
960
The sum of the infinite geometric series 1/2, 1/6, 1/18, ...
3/4
Surprise!
:)