Question

Express the number pattern given below in an algebraic expression 5,9,13,17

Answer 1

5+4=9

9+4=13

13+4=17

17+4=21

Answer 2

Arithmetic Progression - A sequence of numbers in which each differs from the preceding one by a constant difference.

It can be written in the form :

$a_n = a_1 + (n - 1)d$

Given:

$\text{AP} = 5, 9, 13, 17$

Find the first term :

$\text{First Term }= 5$

Find the Common Difference:

$\text{Common Difference }= T_2 - T_1$

$\text{Common Difference }= 9 - 5$

$\text{Common Difference }= 4$

Find the nth term:

$a_n = a_1 + (n - 1)d$

$a_n = 5 + (n - 1) (4)$

$a_n = 5 + 4n - 4$

$a_n = 1 + 4n$

Answer: an = 1 + 4n