Given the Sequence 5, 8, 11, 14, 17, 20 ...
C Write an explicit formula for the given arithmetric sequence. Use your explicit formula the 50th term of the sequence.
an = a1 + (n - 1)d
In this arithmetic sequence, the common difference (d) is 3.
The first term (a1) is 5.
The explicit formula for an arithmetic sequence is: an = a1 + (n - 1)d
Substituting the values into the formula, we get:
an = 5 + (n - 1)3
Simplifying further:
an = 5 + 3n - 3
an = 3n + 2
To find the 50th term (a50), we substitute n = 50 into the formula:
a50 = 3(50) + 2
a50 = 150 + 2
a50 = 152
Therefore, the 50th term of the sequence is 152.