Geometric Sequence Math Example 5

Follow the full solution, then compare it with the other examples linked below.

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Find the 6th term of the geometric sequence: 2, 6, 18, ...

1
Identify the common ratio: $r = \frac{6}{2} = 3$ . Verify: $\frac{18}{6} = 3$ \checkmark
2
Use the formula $a_n = a_1 \cdot r^{n-1}$ with $a_1 = 2$ , $r = 3$ , $n = 6$ .
3
Substitute: $a_6 = 2 \cdot 3^{6-1} = 2 \cdot 3^5 = 2 \cdot 243 = 486$ .

Answer

a_6 = 486

In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio

r

. The general term formula

a_n = a_1 \cdot r^{n-1}

lets you jump directly to any term without computing all the intermediate ones.

About Geometric Sequence

A sequence where each term is obtained from the previous by multiplying by a fixed non-zero constant called the common ratio $r$ .

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