Question

Given the sequence 4, 8, 16, 32, 64, ..., find the explicit formula.

Answer 1

`\sf 2^((n+1))`

Explanation:

Explicit formula is used to represent all the terms of the geometric sequence using a single formula.

`\sf \boxed{\bf t_n=ar^((n-1))}`

Here, a is the first term.

r is the common ratio.

r = second term ÷ first term

4, 8,16,32,64,.....

a = 4

r = 8 ÷4 = 2

`\sf t_n =4*2^((n-1))`

`\sf = 4*2^n * 2^((-1))\\\\ = 4*2^n*(1)/(2)\\\\ = 2*2^n`

`\sf = 2^((n+1))`