Question

Calculate S(68) for the arithmetic sequence a(n) = (2/3)n + 1/6

87/2
273/6
139/3
4,726/3

Answer 1

The standard formula for an A.P. is:
a(n) = a(1) + (n-1)d

=> a(n) = (2/3)n + 1/6
= 5/6 - 4/6 + (2/3)n
= 5/6 - (n-1)(2/3)
Hence, a(1) = 5/6
d = 2/3

Sum formula:

S(n) = (n/2)[2a(1) + (n-1)d]
Plug in the values to get the sum.

Answer 2

I get the last one: 4,726/3