Arithmetic Series
Find the sum of the first 20 terms of the arithmetic sequence:
5,9,13,17,…
S20=860
The first term of an arithmetic sequence is 4, and the common difference is 6. Find the 25th term.
a25=148
Find the sum of the first 6 terms of the geometric sequence:
3,6,12,24,…
S6=189
The third term of a geometric sequence is 16, and the sixth term is 128. Find the common ratio.
r=2
x = 32
x=9
Find the sum of the first 30 terms of the arithmetic sequence:
2,7,12,17,...
S30=2325
The 4th term of an arithmetic sequence is 20, and the 10th term is 50. Find the first term and the common difference.
d=5
The sum of the first 5 terms of a geometric series is 242, and the first term is 2. The common ratio is 3. Verify the sum.
S5=242 (Correct)
Write the nth term from the given information:
a5= 486 r = 3
an=6⋅3(n−1)
(x-2)2
x2 -4x +4
Find the sum of the first 72 terms of the arithmetic sequence:
2,7,12,17,…
s72 = 12,924
In an arithmetic sequence, the 5th term is 25, and the 12th term is 74. Find the first term.
a1=4
Find the sum of the first 7 terms of the geometric sequence:
2,6,18,54,…
S7=2186
Given:
a1=4 r=2
Find the 6th term of the geometric sequence.
a6=128
Factor: x2 +9x +20
(x+4)(x+5)
A student saved $5 in the first week and increased their savings by $3 each week. How much will they have saved in total after 20 weeks?
$710
The 10th term of an arithmetic sequence is 32, and the 25th term is 77. Find the common difference.
d=2
Find the sum of the first 6 terms of the geometric series:
3,6,12,24,…
S6=189
Find the 8th term of the geometric sequence:
2,6,18,54,…
a8=437
x2−6x+5=0
Solve using the quadratic formula
x=5,x=1
The sum of the first 10 terms of an arithmetic sequence is 400, and the first term is 7. Find the common difference.
d=9
3,8,13,18,…
Write the rule for the nth term.
an = 5n-2
Find the sum of the first 7 terms of the geometric series:
5,15,45,135,...
S7=16,405
Write the formula for the nth term of the geometric sequence:
4,12,36,108,…
an=4⋅3(n−1)
4x−7=21
Solve for x
x = 7