The first two terms of an arithmetic progression are 21 and 18.If the sum of the first th term is -24.Find the value of
If you know the the first two terms, you know the initial term and the common difference. This Wikipedia article then gives you the formula for the sum of n terms, so you have to solve the equation for n.
The formula for a sum of a finite arithmetic series is:
In this formula, is the first term. n is the number of terms. d is the common difference (the rate at which the series progresses).
We know that the first term is 21, and we know that the common difference is -3, and that the sum of this series is -24.
Therefore, we have:
now we solve for n:
divide by three to get:
Therefore:
or
or
Since we cant have a negative number of terms, -1 is not a valid answer. Thus, we have :