The first term of an arithmetic progression is 7 and the 100th term is 502. Find the sum of the first 50 terms.

7+99d = 502

50/2 (14+49d) = _____

Not understanding what you just did oobkeck

In that case, you need to review APs, and the formula for the sum of the first n terms -- which I gave you. I just wrote the facts they gave in algebra.

Find d, then use it in the formula.

To find the sum of the first 50 terms of an arithmetic progression, we need to use the formula for the sum of an arithmetic series.

The formula for the sum of an arithmetic series is given by:

Sn = (n/2)(2a + (n-1)d),

where:
- Sn is the sum of the first n terms,
- a is the first term,
- n is the number of terms,
- d is the common difference.

In this case, we are given the first term a = 7, and the 100th term as 502. We need to find the common difference d and the number of terms n.

To find the common difference d, we can use the formula:

an = a + (n-1)d,

where:
- an is the nth term.

Given that a = 7 and an = 502, we can substitute these values into the formula to solve for d:

502 = 7 + (100-1)d.
502 = 7 + 99d.
495 = 99d.
d = 5.

Now that we have found the common difference d, we can substitute it back into the equation to find the number of terms n:

502 = 7 + (n-1)5.
502 = 7 + 5n - 5.
502 - 7 = 5n - 5.
495 = 5n.
n = 99.

Now we have the values for a = 7, d = 5, and n = 99. We can substitute these values into the formula for the sum of an arithmetic series:

Sn = (n/2)(2a + (n-1)d).
S50 = (50/2)(2(7) + (50-1)(5)).
S50 = 25(14 + 49(5)).
S50 = 25(14 + 245).
S50 = 25(259).
S50 = 6475.

Therefore, the sum of the first 50 terms of the arithmetic progression is 6475.