Question

Calculate S58 for the arithmetic sequence {an}= {(5/6(n+(1/3)} If you could show me the steps that would be great. I keep following the directions in the lesson and getting 8,613/3 but all I have to choose from for answers are
146/2
91/2
8,671/6
9,267/6
Thank you!!

Answer 1

We need the first term. Replace n with 1 and simplify

a_n = (5/6)*(n+(1/3))

a_1 = (5/6)*(1+(1/3))

a_1 = (5/6)*( (3/3) + (1/3) )

a_1 = (5/6)*( 4/3 )

a_1 = (5*4)/(6*3)

a_1 = 20/18

a_1 = 10/9

Now we need the 58th term.

Repeat the steps done above, but now use n = 58

a_n = (5/6)*(n+(1/3))

a_58 = (5/6)*(58+(1/3))

a_58 = (5/6)*( (174/3) + (1/3) )

a_58 = (5/6)*( 175/3 )

a_58 = (5*175)/(6*3)

a_58 = 875/18

Next, add up the first and last terms of the sequence we want. So add up a_1 and a_58

a_1 + a_58 = (10/9) + (875/18)

a_1 + a_58 = (20/18) + (875/18)

a_1 + a_58 = (20+875)/18

a_1 + a_58 = 895/18

Multiply this result by n/2 where n = 58

n/2 = 58/2 = 29

(n/2)*(a_1+a_58) = 29*(895/18)

(n/2)*(a_1+a_58) = 25955/18

The answer I'm getting is 25955/18

Because this answer is not listed, I'm thinking there must be a typo somewhere. Please update the problem.