Question

How do you find the indicated term of the geometric sequence where `a_1=16,807`, r=3/7, n=6?

Answer 1

`T_n = T_6 = 243`

Explanation:

General form of geometric sequence is `a, ar, ar^2, ar^3, . . . a r^(n-1)`
`T_n = a r^(n-1)` where 'a' stands for first term `a_1`
Given `a_1 = 16807, r = (3/7) & n = 6`
`:. T_6 = 16807 * (3/7)^(6-1)`
`T_6 = (16807 * 3^5) / 7^5`
`T_6 = (cancel(16807) *243) / cancel(7^5)` as `7^5 = 16807 & 3^5 = 243`
`T_6 = 243`