Find the sum of the first 33 terms of the arithmetic sequence whose first term is 3 and whose 33rd term is -253

As you (should) know,

Sn = n/2 (a1 + an)
S33 = 33/2 (a1 + a33)
= 33/2 (3 - 253)
= 33/2 (-250)
= -33*125 = -4125

To find the sum of the first 33 terms of an arithmetic sequence, we can use the formula for the sum of an arithmetic series.

The formula for finding the sum of the first n terms of an arithmetic series is:

Sn = n/2 * (a + L),

where Sn is the sum of the first n terms, a is the first term, and L is the last term of the sequence.

Given:
First term, a = 3,
Last term, L = -253.

We need to find the sum of the first 33 terms, so n = 33.

Substituting the values into the formula, we have:

Sn = 33/2 * (3 + (-253)).

Simplifying the equation:

Sn = 33/2 * (-250).

Now, we can calculate the sum:

Sn = -4125.

Therefore, the sum of the first 33 terms of the arithmetic sequence is -4125.

To find the sum of the first 33 terms of an arithmetic sequence, we can use the formula for the sum of an arithmetic series, which is:

Sn = n/2 * (a1 + an)

where Sn is the sum of the series, n is the number of terms, a1 is the first term, and an is the nth term.

In this case, we are given that the first term (a1) is 3 and the 33rd term (an) is -253. We need to find the sum of the first 33 terms (n = 33).

First, let's substitute the given values into the formula:

Sn = n/2 * (a1 + an)
= 33/2 * (3 + (-253))

Next, simplify the expression:

Sn = 33/2 * (-250)
= -8250

Hence, the sum of the first 33 terms of the arithmetic sequence is -8250.