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.
If you just put in a calculator 1/5 it shows you 0.2. 0.2 is equal to one-fifth. One-fifth is 1/5.