Question

Find the 8th term of the geometric sequence whose common ratio is 2/3 and whose first term is 7​

Answer 1

The 8th term of the sequence is 896/2187.

Explanation:

We want to find the 8th term of a geometric sequence whose common ratio is 2/3 and whose first term is 7.

We can write a direct formula. Recall that the direct formula of a geometric sequence is given by:

`\displaystyle x_(n) = a\left(r\right)^(n-1)`

Where a is the initial term and r is the common ratio.

Substitute:

`\displaystyle x_(n) = 7\left((2)/(3)\right)^(n-1)`

To find the 8th term, let n = 8. Substitute and evaluate:

`\displaystyle \begin{aligned} x_(8) &= 7\left((2)/(3)\right)^((8) - 1) \\ \\ &= 7\left((2)/(3)\right)^(7) \\ \\ &= 7\left((128)/(2187)\right) \\ \\ &= (896)/(2187) = 0.4096...\end{aligned}`

In conclusion, the 8th term of the sequence is 896/2187.