The fourth term in the sequence that is defined as a_(1) = 3 and a_(n) = 4a_(n-1)+2 is 234
<h3>How to determine the fourth term in the sequence that is defined?</h3>
The definition of the sequence is given as
a_(1)=3
a_(n)=4a_(n-1)+2
The above definition implies that:
The current term of the sequence is calculated by getting the values of n
To determine the fourth term in the sequence that is defined, we set the value of n to 4
i.e. n = 4
So, we have
a_(4) = 4a_(4-1) + 2
a_(4) = 4a_(3) + 2
Calculate a3
a_(3) = 4a_(2) + 2
Calculate a2
a_(2) = 4a_(1) + 2
So, we have
a_(2) = 4 x 3 + 2
a_(2) = 14
Substitute a_(2) = 14 in a_(3) = 4a_(2) + 2
a_(3) = 4 x 14 + 2
a_(3) = 58
Substitute a_(3) = 58 in a_(4) = 4a_(3) + 2
a_(4) = 4 x 58 + 2
a_(4) = 234
Remove the brackets
So, we have
a4 = 234
Hence, the fourth term in the sequence that is defined as a_(1) = 3 and a_(n) = 4a_(n-1)+2 is 234
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