Question

Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. 5, 10, 15, 20, ... an =

Answer 1

Answer:

an = 5n

Explanation:

The sequence goes up by 5 each time, so we can represent it using the formula:

an = 5n

Where n represents the position of the term in the sequence. To find a specific term, we substitute the value of n into the formula. For example, to find the 6th term:

a6 = 5(6)
a6 = 30

So the 6th term in the sequence is 30.

Answer 2

`a_(n)` = 5n

Explanation:

there is a common difference between consecutive terms, that is

10 - 5 = 15 - 10 = 20 - 15 = 5

this indicates the sequence is arithmetic with nth term

`a_(n)` = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = 5 and d = 5 , then

`a_(n)` = 5 + 5(n - 1) = 5 + 5n - 5 = 5n