How many first terms of (10,18,26,34,\ldots) have sum (130)?
Answer and explanation
Correct answer: \(5\)
This is an arithmetic progression with first term \(a=10\) and common difference \(d=8\). The sum of \(n\) terms is \(S_n=\frac{n}{2}[2a+(n-1)d]\). So, \(130=\frac{n}{2}[20+8(n-1)]\), which gives \(n=5\). Indeed, the first five terms \(10,18,26,34,42\) add up to \(130\). The sum of six terms would be \(180\), so it is not correct. Exam tip: when the number of terms is unknown, substitute the given sum in the AP sum formula and solve for \(n\).
Frequently asked questions
What is the correct answer to this question?
\(5\)
Why is this the correct answer?
This is an arithmetic progression with first term \(a=10\) and common difference \(d=8\). The sum of \(n\) terms is \(S_n=\frac{n}{2}[2a+(n-1)d]\). So, \(130=\frac{n}{2}[20+8(n-1)]\), which gives \(n=5\). Indeed, the first five terms \(10,18,26,34,42\) add up to \(130\). The sum of six terms would be \(180\), so it is not correct. Exam tip: when the number of terms is unknown, substitute the given sum in the AP sum formula and solve for \(n\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sequences.
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