im stuck on this help.?

Question

i have to find the sum of the arithmetic sequence given the data well. i have the two formulas but how do i do this one?
a(n)=5; d=-2; n=12

i am given a(n) instead of a(1).. how do i do this one?

what i have there,,, that is the information i was given.
d= -2
n= 12
a(n)= 5

i have to find the sum of the arithmetic sequence from that information.

Answer 1

Find the first term. You have the last term. Now, just plug it into the formula for a(n) to find a(1).

a(n) = a(1) + (n - 1)d
5 = a(1) + (12 - 1)(-2)
5 = a(1) + (11)(-2)
5 = a(1) - 22
27 = a(1)

Now, given the information provided and a(1), which we have calculated, the complete sequence must be this:

27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5.

Remember the formula for the sum of an arithmetic sequence is:

S = n/2 [a(1) + a(n)]. Why?

We have calculated a(1). We are given a(n) = 5, and we know n = 12. Now all we have to do is plug these into the above formula to crank out S.

S = (12/2)(27 + 5)
S = 6(27 + 5)
S = 6(32)
S = 192

To verify our result, we can do this:

27 + 5 = 32
25 + 7 = 32
23 + 9 = 32
21 + 11 = 32
19 + 13 = 32
17 + 15 = 32
15 + 17 = 32
13 + 19 = 32
11 + 21 = 32
9 + 23 = 32
7 + 25 = 32
5 + 27 = 32
_________

S + S = (12)(32)
2S = 384

Notice that we have paired each term in ascending order starting from a(1) with a term in descending order starting from a(n). Thus we have [a(1) + a(n)], [a(2) + a(n - 1)], [a(3) + a(n - 2)] and so forth. Also, notice that each pair sums to [a(1) + a(n)]. Thus we have n pairs of numbers totalling [a(1) + a(n)]. Since we are actually adding all of the elements together twice, and thus get 2S, we must divide that sum by 2 to get S.

2S = n[a(1) + a(n)]
S = {n [a(1) + a(n)]} / 2

Substituting the values above into this last equation, we get this:

S = {12 [27 + 5]} / 2
S = {12 [32]} / 2
S = 384 / 2
S = 192

Answer 2

What exactly is the sequence? What is d? What is n?

Is the sequence ... ,5, 5, 5, 5, ... ?

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a(n) can't be constant if there's a difference of -2.