The first term of an arithmetic progression is \(-2222\) and the common difference is 17. Find the value of the first positive term.
Solution
Let the first term be \(a = -2222\) and the common difference be \(d = 17\). The \(n\)-th term of an arithmetic progression is given by:
\(a_n = a + (n-1) imes d\)
We need to find the smallest \(n\) such that \(a_n > 0\).
\(-2222 + (n-1) imes 17 > 0\)
\((n-1) imes 17 > 2222\)
\(n-1 > \frac{2222}{17}\)
\(n-1 > 130.7\)
Since \(n\) must be an integer, \(n = 132\).
Now, calculate the 132nd term:
\(a_{132} = -2222 + 131 imes 17\)
\(a_{132} = -2222 + 2227\)
\(a_{132} = 5\)
Thus, the first positive term is 5.
Log in to record attempts.