Suppose you are given the arithmetic sequence 3,6,9,...,99.What is the sum of the terms of this sequence?

The formula of an arithmetic sequence is n(a+z)/2 where a is the first term of the sequence and z is the last term of the sequence. n is the number of terms in a sequence. So in this problem, there would be (99-3)/3 + 1 terms. Which is 33. the first term is 3 and the last term is 99 meaning it would be 3 + 99. then plug the numbers in we would get 33(3+99)/2. which is 33(102)/2 which simplifies to 33(51). 33 x 51 is 1683. So 1683 would be our answer.

Suppose you are given the arithmetic sequence 3,6,9,...,99 . What is the sum of the terms of this sequence?

Very gooooooood

since the difference is 3, there are (99-3)/3 + 1 = 33 terms

S33 = 33/2 (3+99)

Well, let's take a clownish approach to solve this! The first term is 3, the last term is 99, and we are dealing with an arithmetic sequence. So, to find the sum, we need to figure out how many terms exist in this sequence. We can do that by dividing the difference between the last term and the first term by the common difference, which is 3.

(99 - 3) / 3 = 96 / 3 = 32

So, we have 32 terms in this sequence. Now, to find the sum, we can use the formula for the sum of an arithmetic sequence:

Sum = (n/2) * (first term + last term)

Plug in the values:

Sum = (32/2) * (3 + 99)

Sum = 16 * 102

That gives us a sum of 1632. Voila!

To find the sum of the terms of an arithmetic sequence, you can use the formula:

Sum = (n/2) * (first term + last term),

where n is the number of terms.

In this case, the first term is 3, the last term is 99, and the common difference is 6 - 3 = 3.

To find the number of terms, we can use the formula:

n = (last term - first term) / common difference + 1.

Applying this formula to our problem, we have:

n = (99 - 3) / 3 + 1
= 96 / 3 + 1
= 32 + 1
= 33.

Now, we can substitute n = 33, first term = 3, and last term = 99 into the sum formula:

Sum = (n/2) * (first term + last term)
= (33/2) * (3 + 99)
= 16.5 * 102
= 1683.

Therefore, the sum of the terms in the arithmetic sequence 3, 6, 9, ..., 99 is 1683.