Question

25 points Find the missing term in of the following arithmetic sequence …-2,____456,….

Answer 1

Answer:

227

Step-by-step explanation:

nth term = a₁ + (n - 1)d

where a1 = first term , n = # of terms and d = common difference.

here we need to solve for the common difference so we can find the missing term, we do so by plugging in what we are given and solving for d

here we are given an nth term, 456 and we are given the first term, -2.

and from what we see there are 3 terms

So we have nth term = 456 , a1 = -2 and n = 3

==> plug these values into the formula

456 = -2 + (3-1)d

==> add 2 to both sides

458 = (3-1)d

==> subtract 1 from 3

458 = 2d

==>divide both sides by 2

d = 229

We then add the common difference to the term before the missing term to get the missing term

-2 + 229 = 227