Arithmetic Sequence
Determine if each sequence is arithmetic. If yes, find the common difference.
5,9,13,17,21,25,…
Yes, the common difference is 4
Find an equation for the general term of the given geometric sequence and use it to calculate its 10th term
3,6,12,24,28....
a10=1536
What is the sum of the first 100 positive odd numbers?
10,000
Find the 10th term of the geometric series 1 + 4 + 16 + 64 + ...
262,144
Evaluate:
12!/6!
665,280
Find the first five terms of the sequence with the given first term and common difference
a1=11
d=7
Find the general term of a geometric sequence where a2= -2 and a5=2/125
an=10(-1/5)^n-1
Find the partial sum of the arithmetic series below
7+12+17+22+...+187
3,589
Find the sum of the following geometric series: i) 1 + (1/3) + (1/9) + ... + (1/2187) ii) 1 + (1/3) + (1/9) + ... using the formula for a geometric series.
3/2
Expand using the binomial theorem:
(x+2)⁵
x⁵+10x⁴+40x³+80x²+80x+32
Find the 21st term of a sequence where the first term is 3 and the common difference is 8
163
19,683
The 15th term of the arithmetic sequence is 33 and the 50th term is 103. What is the 79th partial sum of the arithmetic sequence?
6,557
Find the sum of the first seven (7) terms of the geometric series
2+8+32+…
10,922
Expand using binomial theorem and pascalś triangle
(2x-5)⁴
16x⁴-160x³+600x²-1000x+625
Find the sum of first 50 terms whose general term is given
an= 5n-1
6,325
Find the sum of the first 15 terms of the geometric sequence 1, 1/2, 1/4, 1/8, .... Round your answer to 5 decimals.
1.99994
The 7th term of the arithmetic sequence is −19 and the 13th term is 35. What is the 30th partial sum of the arithmetic sequence?
1,725
Find the sum of the first six (6) terms of the geometric series.
-6+4-8/3+...
-266/81
10!
3,628,800
Find the twelfth term of a sequence where the seventh term is 10 and the common difference is −2. Give the formula for the general term.
an=-2n+24
Sum the first 4 terms of 10, 30, 90, 270, 810, 2430, ...
400
The 9th term of an arithmetic sequence is 57 while its 18th partial sum is 1,080. Find the sum of the first 31 terms of the sequence.
3,069
Write as a fraction: 1.181818…
1+2/11
n!/(n-2)!
n²-n