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Read MoreFind the sum of all natural numbers lyin | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions
Q2. Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
The natural numbers lying between 100 and 1000, which are multiples of 5, are 105, 110, … 995.
This sequence forms an A.P.
Here, first term, a = 105
Common difference, d = 5
Here,
\begin{align} a + (n - 1)d = 995 \end{align}
\begin{align} => 105 + (n - 1)5 = 995 \end{align}
\begin{align} => (n - 1)5 = 995 - 105 = 890 \end{align}
\begin{align} => n -1 = 178 \end{align}
\begin{align} => n = 179 \end{align}
\begin{align} S_n = \frac {n}{2}\left[2a + (n -1)d\right]\end{align}
\begin{align} \therefore S_n = \frac {179}{2}\left[2 × (105) + (179 -1)×(5)\right]\end{align}
\begin{align} = \frac {179}{2}\left[2(105) + (178)(5)\right]\end{align}
\begin{align} = 179\left[105 + (89)5\right]\end{align}
\begin{align} = (179)\left[105 + 445\right]\end{align}
\begin{align} =179 × 550 \end{align}
\begin{align} = 98450 \end{align}
Thus, the sum of all natural numbers lying between 100 and 1000, which are multiples of 5, is 98450.
Study Tips for Answering NCERT Questions:
NCERT questions are designed to test your understanding of the concepts and theories discussed in the chapter. Here are some tips to help you answer NCERT questions effectively:
- Read the question carefully and focus on the core concept being asked.
- Reference examples and data from the chapter when answering questions about Sequence and Series.
- Review previous year question papers to get an idea of how such questions may be framed in exams.
- Practice answering questions within the time limit to improve your speed and accuracy.
- Discuss your answers with your teachers or peers to get feedback and improve your understanding.
Important Questions & Answers
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What is the correct answer to: Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.?
The natural numbers lying between 100 and 1000, which are multiples of 5, are 105, 110, … 995.
This sequence forms an A.P.
Here, first term, a = 105
Common difference, d = 5
...
How do you solve Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5. step by step?
Step-by-step explanation:
• The natural numbers lying between 100 and 1000, which are multiples of 5, are 105, 110, … 995
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