a.
has an average value on [5, 11] of

b. The mean value theorem guarantees the existence of
such that
. This happens for

The first five terms of the sequence are 1, 4, 7, 10, 13.
Solution:
Given data:


General term of the arithmetic sequence.
, where d is the common difference.
d = 3

Put n = 2 in
, we get



Put n = 3 in
, we get



Put n = 4 in
, we get



Put n = 5 in
, we get



The first five terms of the sequence are 1, 4, 7, 10, 13.
Let me see if I am correct I will get back to u