The first and last terms of an A.P is 7.5 and 93 respectively the common difference is 4.5 Find the sum of the series?

Goldenman34

2 years ago

Let's denote the number of terms in the arithmetic series as n. We are given the first term (a = 7.5), the last term (l = 93), and the common difference (d = 4.5).

We can find the number of terms (n) using the formula for the last term of an arithmetic series:

l = a + (n - 1) * d

Here, we have:

93 = 7.5 + (n - 1) * 4.5

Solve for n:

n - 1 = (93 - 7.5) / 4.5
n - 1 = 19
n = 20

Now that we know the number of terms (n), we can find the sum of the series using the formula for the sum of an arithmetic series:

Sum = n * (a + l) / 2

Substitute the known values:

Sum = 20 * (7.5 + 93) / 2
Sum = 20 * 100.5 / 2
Sum = 930

Therefore, the sum of the arithmetic series is 930.