The sum of the first 10 terms of an Arithmetic Progression is 250. If the first term is 15, what is the 10th term?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 35
The sum of an arithmetic progression is the number of terms times the average of the first and last terms: \(S_{n}=\frac{n}{2}(a+l)\). With the sum, \(n\) and \(a\) known, the only unknown in this formula is the last term, here the 10th term.
Putting in \(S_{10}=250\), \(n=10\) and \(a=15\): \(\displaystyle250=\frac{10}{2}(15+l)\)
So \(15+l=50\), and the 10th term is \(l=\) 35