Question

What is the explicit formula for this sequence? 2,10,50,250,1250
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Answer 1

This is a geometric sequence with a₁ = 2 and r = 5 where a₁ is the first term and r is the common ratio.

Explicit formula: aₙ = a₁ * r ⁿ⁻¹

The answer is aₙ = 2 * (5ⁿ⁻¹)

Answer 2

`a_n = 2(5)^(n-1)`

Explanation:

Explicit Geometric Formula:
`a_n = a_1r^(n-1)`

a₁ is 1st term

r is common ratio

n is term number

Step 1: Find common ratio r

r = 10/2 = 5

Step 2: Plug variables into formula

`a_n = 2(5)^(n-1)`