An Arithmetic sequence whose first term is 102 and common difference is -3 has its 7th term as _______.
To find the 7th term of an arithmetic sequence, we use the formula:
\(a_n = a_1 + (n-1)d\)
Where:
\(a_n\) is the nth term of the arithmetic sequence,
\(a_1\) is the first term of the arithmetic sequence,
\(n\) is the position of the term in the arithmetic sequence, and
\(d\) is the common difference of the arithmetic sequence.
Given that the first term (\(a_1\)) is 102 and the common difference (\(d\)) is -3, we can substitute these values into the formula to find the 7th term:
\(a_7 = 102 + (7-1)(-3)\)
\(a_7 = 102 + (6)(-3)\)
\(a_7 = 102 - 18\)
\(a_7 = 84\)
Therefore, the 7th term of the arithmetic sequence is 84.