The first and last term of an ap are 0 and 108 if the sum of the sequence is 702 find
(a) the number of terms of the sequence
(b) the common difference
Let's denote the number of terms in the sequence as n and the common difference as d.
We know that the first term is 0 and the last term is 108. The formula for the sum of an arithmetic sequence is given by:
Sum = (n/2)(first term + last term)
So we can write:
702 = (n/2)(0 + 108)
702 = 54n
Dividing both sides of the equation by 54, we get:
n = 13
Therefore, there are 13 terms in the sequence.
To find the common difference, we can use the formula:
Last term = first term + (n - 1) * common difference
Plugging in the values we know, we have:
108 = 0 + (13 - 1) * d
108 = 12d
Dividing both sides of the equation by 12, we get:
d = 9
So the common difference is 9.