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Chapter 5 · Question 4

State the formula for the sum of first nn terms of an AP. Find the sum of first 20 natural numbers.

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Q4

State the formula for the sum of first nn terms of an AP. Find the sum of first 20 natural numbers.

Answer Revealed
Direct Answer:
The sum is Sn=n2[2a+(n−1)d]S_n=\frac n2[2a+(n-1)d] or Sn=n2(a+l)S_n=\frac n2(a+l). For natural numbers, a=1a=1, d=1d=1, n=20n=20, so S20=202(1+20)=210S_{20}=\frac{20}{2}(1+20)=210.

Simple Explanation

Use Sn=n(a+l)/2S_n=n(a+l)/2. The first 20 natural numbers add to 210210.

Exam-Ready Structure

For an AP, Sn=n2[2a+(n−1)d]S_n=\frac n2[2a+(n-1)d]. If the last term ll is known, Sn=n2(a+l)S_n=\frac n2(a+l). For 1,2,3,…,201,2,3,\ldots,20, a=1a=1, l=20l=20, n=20n=20. Therefore S20=202(1+20)=10×21=210S_{20}=\frac{20}{2}(1+20)=10\times21=210.

Key Points

  • The sum is Sn=n2[2a+(n−1)d]S_n=\frac n2[2a+(n-1)d] or Sn=n2(a+l)S_n=\frac n2(a+l).
  • Use the NCERT formula or theorem carefully.
  • Write units and final conclusion where applicable.

Related Questions

Q5

Reena starts with a monthly salary of ₹8000 and gets an annual increment of ₹500. What will be her salary in the 10th year?

Q6

Find the sum of the first 15 terms of the AP 5,8,11,…5,8,11,\ldots.

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