What is the sum of the 12 terms of AP if a1+a5+a8+a12=24 ?

We'll write the sum of 12 terms of an arithmetical
progression:

S12 = (a1 +
a12)*12/2

We'll have to determine the sum a1 + a12, for
finding S12.

We also know, from enunciation, that
a1+a5+a8+a12=24.

According to the
rule:

(a1 + a8)/2 = (a5 +
a12)/2

Since the ratios are equal, we'll interchange the
terms:

a1 + a12 = a5 +
a8

We'll substitute a5 + a12 into the
sum:

a1 + a12 + a1 + a12 =
24

2(a1 + a12) = 24

a1 + a12 =
12

S12 =
12*12/2

The sum is: S12 =
72