June 2018 Paper 2H Question 23
2 The sum of the first 48 terms of an arithmetic series is 4 times the
sum of the first 36 terms of the same series.
Find the sum of the first 30 terms of this series.
(Total for Question 2 is 5 marks)

In an arithmetic series, the sum of the first n terms can be calculated using the formula , where is the first term, is the common difference, and is the number of terms. Here, the sum of the first 48 terms, , is 4 times the sum of the first 36 terms, . Setting up the equation:

yields:

This simplifies down to:

Let’s solve this equation to find relations among and .

After simplifying, we find . Solving gives us:

Now, substituting back into the formula for :

To finalize the value of , we would need further information regarding the specifics of either term in the sequence. Whatever it is, will ultimately depend on the value of . However, if you have or details tying to it, plug that in to get the exact total for .