JEE Mains · Maths · STD 11 - 8. sequence and series
Different \(A.P.\)'s are constructed with the first term \(100\),the last term \(199\),And integral common differences. The sum of the common differences of all such, \(A.P\)'s having at least \(3\) terms and at most \(33\) terms is.
- A \(54\)
- B \(52\)
- C \(56\)
- D \(53\)
Answer & Solution
Correct Answer
(D) \(53\)
Step-by-step Solution
Detailed explanation
\(1^{\text {st }} \text { term }=100=a\) Last term \(=199=\ell\) If \(3\) term \(a, a+d, a+2 d\) \(a _{ a }=\ell= a +( n -1) d\) \(d _{ i }=\frac{\ell- a }{ n - l }\) \(n \rightarrow\) number of terms \(n =3, d _{1}=\frac{199-100}{2}\) \(=\frac{99}{2} \notin I\)…
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