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

Question

asked Apr 26, 2023 85.4k views

1 Answer

Mukesh Gupta · Answer 1 · 2023-05-01T18:23:01+0000

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