Question

Examine the sequence of values below. 653, 1261, 1869, 2477, 3085, 3693 Which algebraic expression represents the nth value in this sequence?

Answer 1

Answer: $a_{n}=653+(n-1)608$

Step-by-step explanation: This sequence of numbers is an arithmetic progression: a sequence of numbers in which the last number is the previous number plus a constant factor.

For example, the sequence:

653 1261 1869 2477 3085 3693

if you subtract each term with its previous number, the result will be 608:

1261 - 653 = 608

1869 - 1261 = 608

...

33693 - 3085 = 608

For a general arithmetic progression, the nth value is

$a_{n}=a_{0}+(n-1)r$

where

$a_{n}$ is the wanted value

$a_{0}$ is the first value

n is number of terms or values

r is constant factor

For the sequence above, nth value is:

$a_{n}=653+(n-1)608$

The algebraic expression for the nth value in this sequence is $a_{n}=653+(n-1)608$.