Question

Given a geometric sequence with a1 = 6 and r= 2/3 write an explicit formula for an the nth term of the sequence.​

Answer 1

the explicit formula for aₙ the nth term of the sequence will be:$a_{n}=6\times (\frac{2}{3})^{n-1}$

Step-by-step explanation:

The explicit formula of geometric sequence is of the form:

$a_{n}=a_{1}r^{n-1}$

where a₁ is the first term and r is the common ratio.

We are given:

a₁ = 6

r = 2/3

Putting values in the formula:

$a_{n}=a_{1}r^{r-1}\\a_{n}=6\times (\frac{2}{3})^{n-1}$

So, the explicit formula for aₙ the nth term of the sequence will be: $a_{n}=6\times (\frac{2}{3})^{n-1}$

Keywords: Explicit formula for geometric sequence

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