Question

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

Answer 1

Answer:

$\sf 2^{(n+1)}$

Step-by-step 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

$\sf t_n =4*2^{(n-1)}$

    $\sf = 4*2^n * 2^{(-1)}\\\\ = 4*2^n*\dfrac{1}{2}\\\\ = 2*2^n$

   $\sf = 2^{(n+1)}$