lf the first of an AP is 7 and 80th term is 393,find the sum of the first 80 terms
S = 80/2 (7+393)
To find the sum of the first 80 terms of an arithmetic progression (AP), you can use the formula:
Sn = (n/2) * (2a + (n - 1)d)
Where Sn represents the sum of the first n terms, a is the first term, n is the number of terms, and d is the common difference.
In this case, the first term (a) is given as 7 and the 80th term is given as 393. We need to find the sum of the first 80 terms (Sn).
First, let's determine the common difference (d). The common difference (d) is the difference between any two consecutive terms in an arithmetic progression.
We can find d by using the formula:
d = (an - a) / (n - 1)
Given that the first term (a) is 7, the 80th term (an) is 393, and n is 80:
d = (393 - 7) / (80 - 1)
d = 386 / 79
d ≈ 4.891
Now that we have the common difference (d), we can substitute the values into the sum formula:
Sn = (n/2) * (2a + (n - 1)d)
Sn = (80/2) * (2*7 + (80 - 1)*4.891)
Sn = 40 * (14 + 79*4.891)
Sn = 40 * (14 + 386.489)
Sn = 40 * 400.489
Sn ≈ 16019.56
Therefore, the sum of the first 80 terms of the given arithmetic progression is approximately 16019.56.