O.
the sum of the first k terms of a sequence is 3k^2 + k.
(a) find the 6th term of the sequence.
(b) determine whether the sequence is an arithmetic sequence.

(a) 34.

(b) Yes.

Step-by-step explanation:

The first term is 3(1)^2 + 1 = 4 ( where k = 1).

The sum of 2 terms =  3(2)^2 + 2 = 14.

The sum of 3 terms = 3(3)^2 + 3 = 30.

The sum of 4 terms = 3(4)^2 + 4 = 52.

So the first 4 terms are 4, 10, 16 and 22 .     - increasing by 6.

The common difference is 6 so it is an arithmetic sequence.

The 6th term = a1 + d(n - 1)

= 4 + 6(6-1)

= 34.

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: