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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

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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

User Mukesh Gupta
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