Question

what is the sum of the arithmetic sequence 3 9 15... if there are 36 terms

Answer 1

first we will find the common difference by subtracting the first term from the second term.
9 - 3 = 6
so our common difference (d) is 6

Now we will find the 36th term because we will need it to find the sum
an = a1 + (n - 1) * d
n = the term we want to find = 36
a1 = first term = 3
d = common difference = 6
now we sub
a36 = 3 + (36 - 1) * 6
a36 = 3 + 35 * 6
a36 = 3 + 210
a36 = 213

now that we know the 36th term. we can find the sum
sn = n(a1 + an) / 2
sn = sum of n terms = 36
a1 = first term = 3
an = 36th term = 213
now we sub
s36 = 36(3 + 213) / 2
s36 = 36 (216) / 2
s36 = 7776/2
s36 = 3888

If I am not mistaken, the sum of the 36 terms is 3888