In an AP, (d=6), (n=18), and (S_{18}=1512). Find the first term (a).
Answer and explanation
Correct answer: 33
Use the sum formula \(S_n=\frac{n}{2}[2a+(n-1)d]\). Thus, \(1512=\frac{18}{2}[2a+17\times6]=9(2a+102)\). Hence \(2a+102=168\), so \(2a=66\) and \(a=33\). If 30 were used as the first term, the sum would be 1458, so it is not correct. Exam tip: In the formula, use \((n-1)d\), not \(nd\).
Frequently asked questions
What is the correct answer to this question?
33
Why is this the correct answer?
Use the sum formula \(S_n=\frac{n}{2}[2a+(n-1)d]\). Thus, \(1512=\frac{18}{2}[2a+17\times6]=9(2a+102)\). Hence \(2a+102=168\), so \(2a=66\) and \(a=33\). If 30 were used as the first term, the sum would be 1458, so it is not correct. Exam tip: In the formula, use \((n-1)d\), not \(nd\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an AP.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
