Question

In Exercises, find a plausible formula for the general term of the given sequence.

$\left\{1,7,13,19,25,\dots \right\}$

Short answer

The plausible formula for the general term of the sequence is$a_{k+1}=a_k+6,$where$a_1=1.$

Step-by-step solution

Step 1. Given information.

The given sequence is$\left\{1,7,13,19,25,\dots \right\}.$

Step 2. plausible formula for the general term. 

the first term of the sequence is $a_1=1.$

The second term of the sequence is $a_2=7=a_1+6.$

similarly, the third term of the sequence is $a_3=13=a_2+6.$

In sequence $\left\{1,7,13,19,25,\dots \right\},$difference between consecutive terms is $6.$

So plausible formula for the general term of the sequence is$a_{k+1}=a_k+6,$where$a_1=1.$