Question

Find an explicit formula for the arithmetic sequence -5,13,31,49

Answer 1

an explicit formula for the arithmetic sequence -5,13,31,49 is  $a_n =18n-23$ .

Step-by-step explanation:

Here we have an arithmetic sequence -5,13,31,49 . We need to find an explicit formula for the arithmetic sequence  .Let's find out:

Let  $a_1 = -5 , a_2=13 ,a_3=31,a_4=49$ be terms of an A.P , common difference is :

⇒ $d=a_2-a_1$

⇒ $d=13-(-5)$

⇒ $d=13+5$

⇒ $d=18$

We know that general term of an Arithmetic Progression ( A.P) is :

⇒ $a_n = a+(n-1)d$

So , Here we will have  $a_n = -5+(n-1)18$

⇒ $a_n = -5+(n-1)18$

⇒ $a_n = -5+18n-18$

⇒ $a_n =18n-23$

Therefore , an explicit formula for the arithmetic sequence -5,13,31,49 is  $a_n =18n-23$ .