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May 5, 2020

Sum of digits | AMC-10A, 2020 | Problem 8

Try this beautiful problem from Algebra based on sum of digits

Sum of digits - AMC-10A, 2020- Problem 8


What is the value nof

\(1+2+3-4+5+6+7-8+......+197+198+199-200\)?

  • \(9800\)
  • \(9900\)
  • \(10000\)
  • \(10100\)
  • \(10200\)

Key Concepts


Algebra

Arithmetic Progression

Series

Check the Answer


Answer: \(9900\)

AMC-10A (2020) Problem 8

Pre College Mathematics

Try with Hints


The given sequence is \(1+2+3-4+5+6+7-8+......+197+198+199-200\). if we look very carefully then notice that \(1+2+3-4\)=\(2\), \(5+6+7-8=10\),\(9+10+11-12=18\).....so on.so \(2,10,18......\) which is in A.P with common difference \(8\). can you find out the total sum which is given....

can you finish the problem........

we take four numbers in a group i.e \((1+2+3-4)\),\((5+6+7-8)\),\((9+10+11-12)\)......,\((197+198+199-200)\). so there are \(\frac{200}{4}=50\) groups. Therefore first term is\((a)\)= \(2\) ,common difference\((d)\)=\(8\) and numbers(n)=\(50\). the sum formula of AP is \(\frac{n}{2}\{2a+(n-1)d\}\)

can you finish the problem........

\(\frac{n}{2}\{2a+(n-1)d\}\)=\(\frac{50}{2}\{2.8+(50-1)8\}\)=\(9900\)

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