a) The given sequence is expressed as
52, 53, 54, 55, .......252
The first step is to determine the type of sequence by comparing the consecutive terms. We can see that there is a common difference, d between the consecutive terms.
d = 53 - 52 = 54 - 53 = 1
This means that it is an arithmetic sequence. The formula for determining the nth term of an arithmetic sequence is expressed as
an = a1 + (n - 1)d
where
an is the nth term of the sequence
n is the number of terms in the sequence
d is the common difference
a1 is the first term
From the information given,
a1 = 52, d = 1, an = 252
thus, we have
252 = 52 + (n - 1)1
252 = 52 + n - 1
252 = 52 - 1 + n = 51 + n
n = 252 - 51
n = 201
There are 201 terms in the sequence
