What is the sum of the first 28 terms of this arithmetic sequence? 69, 75, 81, 87, 93, 99, …

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