precal question

Question

Find the partial sum S_n of the arithmetic sequence that satisfies the given conditions.

a₂ = 7, a₅ = 8.5, n = 16

S₁₆ = 

Answer 1

Hi Viviana,

The formula for the n^th term of an arithmetic sequence is: a_n = a₁ + (n - 1)*d.

With a₂ = 7:

7 = a₁ + (2 - 1)*d

7 = a₁ + d

a₁ = 7 - d

With a₅ = 8.5

8.5 = a₁ + (5 - 1)*d

8.5 = a₁ + 4d

a₁ = 8.5 - 4d

Setting a₁ = a₁:

7 - d = 8.5 - 4d

3d = 1.5

d = .5

And therefore a₁ = 7 - d = 7 - .5 = 6.5

And a₁₆ = 6.5 + (16 - 1)*.5 = 14

The formula for the arithmetic sum is S_n = n(a₁ + a_n)/2.

S₁₆ = 16(6.5 + 14)/2 = 8*20.5 = 164

I hope this helps, Joe.