Find the value of the term in the arithmetic sequence using an = a^1+ (n-1)d. 3,5,7,9,11, (8th term)

Work Shown:

a1 = 3 = first term

d = 2 = common difference (since we add 2 to each term to get the next one)

Let's compute the nth term.

an = a1 + (n-1)*d

an = 3 + (n-1)*2

an = 3 + 2n-2

an = 2n+1

To check things so far, we can plug in something like n = 2

an = 2n+1

a2 = 2*2+1

a2 = 5

Showing that the 2nd term is 5, which matches with the sequence given to us

Let's check n = 3

an = 2n+1

a3 = 2*3+1

a3 = 7

That matches as well. I'll let you check the others.

Plug in n = 8 to find the 8th term

an = 2n+1

a8 = 2*8+1

a8 = 17

The eighth term is 17, which is the final answer.

You could extend out the given sequence by adding 2 each time until you reach the 8th term

3,5,7,9,11,13,15,17

Though this method is slow if you need to find say the 38th term

17 is the answer for the value of the term in the arithmetic sequence using the above

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

5

step-by-step explanation: