Compute the sums below. (Assume that the terms in the first sum are consecutive terms of an arithmetic sequence.)

9 + 12 + 15 + ... + 336 =

=18975

Step-by-step explanation:

This is an arithmetic sequence

an = a1 + d (n-1)

a1 = 9

d = 12-9 = 3

an = 9 + 3 (n-1)

The sum of an arithmetic sequence is given by

Sn = n/2 (a1+an)

So we need to determine what number in the sequence 336 is

an = 9 + 3 (n-1)

336 = 9 + 3 (n-1)

Subtract 9 from each side

336-9 = 9+-9 + 3 (n-1)

327 = 3 (n-1)

Divide each side by 3

327/3 = 3/3 (n-1)

109 = n-1

Add 1 to each side

109+1 = n-1+1

110 = n

336 is the 110 term

The sum from 9 to 336

Sn = n/2 (a1+an)

S 110 = 110/2 (9+336)

= 55 (345)

=18975