Math CentralQuandaries & Queries


Question from a student:

the 3rd term of an A.PPP is 10 more than the first term while the 5th term is 15 more than the second. find the sum of the 8th and 15th terms if the 7th term is 7 times the first term.


The defining feature of an arithmetic progression is that there is a number $d$ so that to get from any term to the next you add $d.$ Thus to get to the third term from the first term you add $d$ twice. What is $d?$ Does this agree with "5th term is 15 more than the second"?

Suppose the first term is $a.$ Using the value of $d$ you found above, what is the 7th term? This is 7 times $a.$ What is $a?$


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