Artitmetic sequence question

Question

+1

1419

2

+117

In this particular arithmetic sequence, a8 = 28 and a16 = 108. What is the value of a24?

a24 = 188

a24 = 162

a24 = 198

a24 = 224

I know it's not B

Guest · Answer 1 · 2017-04-14T10:20:24

188 ...........

geno3141 · Answer 2 · 2017-04-14T10:25:10

The general formula is: a_n = a₁ + (n - 1)d

a₈ = 28 ---> a₈ = a₁ + (8 - 1)d ---> 28 = a₁+ 7d

a₁₆ = 108 ---> a₁₆ = a₁ + (16 - 1)d ---> 108 = a₁ + 15d

Subtract down the columns: -80 = - 8d

---> d = 10

Substituting this value for d into the first equation: 28 = a₁+ 7d

---> 28 = a₁+ 7(10)

---> 28 = a₁+ 70

---> a₁ = -42

So the equation is: a_n = -42 + (n - 1)(10)

To find a₂₄, substitue 24 in for n and solve.