Math CentralQuandaries & Queries


Question from Gbenga, a student:

In an A.P the difference between 8th and 4th term is 20. The 8th term is 1\2 times the 4th term . Find arithmetic progression.

Hi Gbenga,

The important feature of an arithmetic progression is that the difference between any two consecutive terms is the same. So if the first term is $a$ and the second term is $a + d$ then the third term is $a + d + d = a + 2d$ and the fourth term is $a + 3d,$ and so on. What is the expression for the $n^{th}$ term?

Write the expression for the fourth term and the eighth term, subtract them, set the difference to 20 and solve for $d.$ Now use the fact that the eighth term is half of the fourth term to find the value of $a.$


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