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

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.

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^

step-by-step explanation: