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अभ्यासक्रम

Sum of First ‘n’ Terms of an Arithmetic Progressions

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CBSE: Class 10
Maharashtra State Board: Class 10
CISCE: Class 10

Formula: Sum of First ‘n’ Terms

If a, n, l are known → \[S_n=\frac{n}{2}(a+l)\]

If a, n, d are known → \[S_n=\frac{n}{2}\left[2a+(n-1)d\right]\]

CBSE: Class 10
Maharashtra State Board: Class 10

Formula: Sum of First n Natural Numbers

\[1+2+\cdots+n=\frac{n(n+1)}{2}\]

Maharashtra State Board: Class 10

Formula: Sum of First n Even Natural Numbers

\[2+4+\cdots+2n=n(n+1)\]

Maharashtra State Board: Class 10

Formula: Sum of First n Odd Natural Numbers

\[1+3+\cdots+(2n-1)=n^2\]

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Shaalaa.com | SUMMATION (SIGMA) NOTATION

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SUMMATION (SIGMA) NOTATION [00:23:21]
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SUMMATION (SIGMA) NOTATION
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SERIES IN SIGMA NOTATION
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Arithmetic Progression part 10 (Sum of n terms of AP)
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Arithmetic Progression part 11 (Example - Sum of n terms of AP)
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Related QuestionsVIEW ALL [525]

The sum of three consecutive terms of an AP is 21 and the sum of the squares of these terms is 165. Find these terms

Read the following passage:

India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs. The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 16000 sets in 6th year and 22600 in 9th year.
  1. In which year, the production is 29,200 sets?
  2. Find the production in the 8th year.
    OR
    Find the production in first 3 years.
  3. Find the difference of the production in 7th year and 4th year.

The 19th term of an AP is equal to 3 times its 6th term. If its 9th term is 19, find the AP. 

In an A.P. the first term is – 5 and the last term is 45. If the sum of all numbers in the A.P. is 120, then how many terms are there? What is the common difference?

Find the sum of first 10 terms of the A.P.

4 + 6 + 8 + .............

Find whether 55 is a term of the A.P. 7, 10, 13,... or not. If yes, find which term is it.

Rs 1000 is invested at 10 percent simple interest. Check at the end of every year if the total interest amount is in A.P. If this is an A.P. then find interest amount after 20 years. For this complete the following activity.

If the sums of n terms of two arithmetic progressions are in the ratio \[\frac{3n + 5}{5n - 7}\] , then their nth terms are in the ratio

  
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