The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?
Number of terms = 38, Sum = 6973
Explanation
This question tests two key concepts from the AP chapter: finding the number of terms using the nth term formula, and finding the sum using the sum formula. Students need to apply both formulas sequentially - first finding n using a_n = a + (n-1)d, then finding S_n using S_n = n/2(a + l).
Solution Steps
Given: First term (a) = 17, Last term (l) = 350, Common difference (d) = 9
Step 1: Find number of terms (n). Using formula for nth term: a_n = a + (n-1)d. Substituting values: 350 = 17 + (n-1) × 9. Solving: 350 - 17 = (n-1) × 9, which gives 333 = (n-1) × 9. Therefore, n-1 = 333/9 = 37, so n = 38.
Step 2: Find sum of all terms. Using sum formula: S_n = n/2(a + l). Substituting values: S_38 = 38/2 × (17 + 350) = = 6973.