If the first term of an AP is (5), the last term is (45), and the number of terms is (9), what is the sum?
Answer and explanation
Correct answer: 225
When the first and last terms are known, the sum of the first \(n\) terms of an AP is \(S_n=\frac{n}{2}(a+l)\). Thus, \(S_9=\frac{9}{2}(5+45)=\frac{9}{2}\times 50=225\). Hence, 225 is correct. A value such as 215 can result from an addition or multiplication error. Exam tip: do not forget to multiply by the number of terms \(n\) in the sum formula.
Frequently asked questions
What is the correct answer to this question?
225
Why is this the correct answer?
When the first and last terms are known, the sum of the first \(n\) terms of an AP is \(S_n=\frac{n}{2}(a+l)\). Thus, \(S_9=\frac{9}{2}(5+45)=\frac{9}{2}\times 50=225\). Hence, 225 is correct. A value such as 215 can result from an addition or multiplication error. Exam tip: do not forget to multiply by the number of terms \(n\) in the sum formula.
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.
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