Geometric
Sequences & Series
A geometric sequence is a set of numbers where the next number is created by multiplying the previous one by another number. A series is when you add up that sequence. Here you'll find more than a dozen solved problems.
Find the common ratio
Find r for the sequence -5, -1.667, -0.556, ...
Find the 8th term
Find T8 in 59049, 19683, 6561, 1287, ...
Find "n" (big numbers!)
Find the number of terms in the given sequence: 6, 42, ..., 1694851494.
Convert to fraction.
Convert : 7 + .7 + .07 + ... + 0.000007
Find the 8th term.
Find the 8th term of 256 + 128 + 64 + ....
Is it positive or negative?
Find S10 for 7 - 35 + 175 - ...
And using fractions ...
Find infinite sum of 27 + 9/2 + 3/4 + ...
A convergent series?
Add this up: 15 + 15(1/7) + 15(1/7)^2 + ....
Do this one in your head!
33 + 33/5 + 33/25 ... Is this convergent or divergent, and does it have a sum?
3 tougher questions
Test out these 3 exam style short answer questions, and you'll be ready for an exam!
A challenging adventure
This problem requires several careful steps to solve. If S1 = 0.7 and S2 = 2.1, determine the sum of the first 12 terms.
Compound interest
An education savings plan earns 5% interest. $4,000 is invested today. Determine the formula for the value after n years, the value after year 1, 2, 3, 4, 9 and 16. When will it double?
Word Problem - Harder!
For a geometric series, S4/S8 = 1/17 and the first term is 3. Find the first 4 terms.
Turn straw into gold!
Write these repeating decimals as fractions, in lowest form:
(A) 0.55555 .... (B) 0.122222 ...