First we find the common difference by subtracting the first term by the second term. 75 - 69 = 6. So the common difference is 6.
now we need to find the 28th term...we need to do this because we need to use this number in the sum formula.
an = a1 + (n-1)*d
n = term to find = 28
a1 = first term = 69
d = common difference = 6
now we sub
a28 = 69 + (28 - 1) * 6
a28 = 69 + 27 * 6
a28 = 69 + 162
a28 = 231...this is the 28th term
now we use the sum formula
sn = (n(a1 + a28) / 2
s28 = (28(69 + 231) / 2
s28 = (28(300) / 2
s28 = 8400/2
s28 = 4200 <===the sum of the first 28 terms
Since the formula for the volume of the cube is width*height*length, we know that 6*12*length=1242. Multiplying it out, we get that 72*length=1242. After that, we can divide 72 from both sides to get 1242/72=length=17.25 inches which I guess is close enough to 17?