Math CentralQuandaries & Queries


Question from loberto, a student:

the 3rd term of an a.p is 10more than the 1st term,while the 5th term is 15more than the 2nd term,find the sum of the 8th and 15th terms of the a.p if the 7th term is 7times the 1st term

Hi Loberto,

Suppose the first term is $a$ and the common difference is $d$ then the first three terms are

$a, a + d, a + 2d.$

If the third term is 10 more than the first term then $a + 2d = a + 10.$ Solving this gives $d = 5.$ Hence each term is $5$ more than the previous term and thus you already know that the fifth term is 15 more than the second term.

You also know that the seventh term is 7 times the first term. What is the seventh term? This is 7 times the first term. What is $a?$


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