• Sequence
• Arithmetic
• Geometric
• nth
• Limit
• P.
• Monotone
• Bounded
• Convergent

A geometric sequence or geometric progression is a sequence of numbers such that the ratios between successive terms is a constant r, called the common ratio.

3, 6, 12, 24, 48, ...

6/3 = 2.

12/6 = 2.

24/12 = 2.

48/24 = 2.

r = 2.

Nth Term of a Geometric Sequence

1If the 1st term is known.

a_n = a₁ · r^n-1

3, 6, 12, 24, 48, ..

a_n = 3 · 2^n-1 = 3 · 2ⁿ · 2^-1 = (3/2)· 2ⁿ

2If the value that occupies any other term of the sequence is known.

a_n = a_k · r^n-k

a₄= 24, k=4 and r=2.

a_n = a₄ · r^n-4

a_n = 24· 2^n-4= (24/16)· 2ⁿ = (3/2) · 2ⁿ

Geometric Series

A geometric series is the sum of a geometric sequence.

Compute the sum of the first 5 terms of the sequence: 3, 6, 12, 24, 48, ...

Infinite Geometric Series

If −1 < r < 1 the infinite geometric series converges to a specific value:

Calculate the sum of the terms of the sequence:

Product

Calculate the product of the first 5 terms of the sequence: 3, 6, 12, 24, 48, ...

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