Write the related series for the finite sequence –13, –8, –3, . . ., 12? Then find the sum.

Answer 1

The related series for the given finite sequence is an arithmetic progression with a common difference of 5.

Using the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference, and n is the term number,

we can find the nth term as:
a_n = -13 + (n-1)5

To find the sum of the series, we can use the formula for the sum of an arithmetic series:
S_n = n/2(a_1 + a_n), where S_n is the sum of the first n terms.

Substituting the values into the equation:
S_n = n/2(-13 + (-13 + (n-1)5))
= n/2(-13 -13 + 5n -5)
= n/2(5n - 26)

To find the sum of the given finite sequence, we need to calculate S_8 (as the sequence has 8 terms):
S_8 = 8/2(5(8) - 26)
= 4(40 - 26)
= 4(14)
= 56

Therefore, the sum of the given finite sequence is 56.

Answer 2

are you sure

Answer 3

I apologize for the incorrect response. You are right, the previous calculation was incorrect.

Let's find the correct sum of the given finite sequence.

The sequence -13, -8, -3, ... can be represented by the formula:
a_n = a_1 + (n-1)d

where a_1 is the first term (-13), d is the common difference (5), and n is the term number.

The last term of the sequence can be found by substituting the values into the formula:
a_n = -13 + (n-1)5
12 = -13 + (n-1)5

Simplifying the equation:
12 = -13 + 5n - 5
12 = -18 + 5n
5n = 30
n = 6

So, the sequence has 6 terms.

Now, let's find the sum of the sequence using the formula for the sum of an arithmetic series:

S_n = n/2(a_1 + a_n)

Substituting the values into the formula:
S_6 = 6/2(-13 + 12)
= 6/2(-1)
= 3(-1)
= -3

Therefore, the sum of the given finite sequence -13, -8, -3, ..., 12 is -3.