Geometric Sequences Calculator

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Example

Created on 2024-06-20Asked by Owen Garcia (Solvelet student)

Find the 5th term of the geometric sequence where the first term

a = 3

and the common ratio

r = 2

Solution

To find the 5th term of the geometric sequence where the first term

a = 3

and the common ratio

r = 2

: The

n

-th term of a geometric sequence is given by:

a_n = a r^{n-1}

For

n = 5

a_5 = 3 \cdot 2^{5-1}

= 3 \cdot 2^4

= 3 \cdot 16

= 48

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1. Find the 10th term of the geometric sequence $3, 6, 12, 24, \,2. Calculate the sum of the first 5 terms of the geometric sequence $2, 6, 18, 54, \.,

DefinitionGeometric sequence is a sequence in which a term is obtained by multiplying the preceding term with a unique number, also known as the common ratio and cannot be zero or finite. Sequences are either function or infinite when mapped out, and they are also known as GEOMETRIC sequence, meaning it is an exponential growth or decay pattern that depends on the common ratio. Finance, computer science, and physics use this sequence for exponential growth, including compound interest or population dynamics. E.g., 2,6,18,54,… is a geometric sequence, with a common ratio of 3, since each term is the previous term times 3.

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