Question

the two arithmetic sequences, 1,5,9,13... and 1,6,11,16.. have infinitely many terms in common. what is the sum of the first three common terms

Answer 1

Arithmetic sequence is modeled by the next formula:

`a_n=a_1+(n-1)\cdot d`

where an is the nth term, a1 is the first term, and d is the common difference.

In the case of the first sequence:

`a_n=1+(n-1)\cdot4`

In the case of the second sequence:

`a_n=1+(n-1)\cdot5`

The 6th term of the first sequence is:

`a_6=1+(6-1)\cdot4=21`

The 5th term of the second sequence is:

`a_5=1+(5-1)\cdot5=21`

The 11th term of the first sequence is:

`a_(11)=1+(11-1)\cdot4=41`

The 9th term of the second sequence is:

`a_9=1+(9-1)\cdot5=41`

Therefore, the first three common terms are: 1, 21, and 41. And the sum of them is 63