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Class 10MathematicsArithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APEasy
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What will be the sum of the first (10) terms of the AP (7,14,21,\ldots)?

Answer and explanation

Correct answer: 385

Here, the first term is \(a=7\), the common difference is \(d=7\), and \(n=10\). The tenth term is \(a_{10}=7+(10-1)\times7=70\). Therefore, \(S_{10}=\frac{10}{2}(7+70)=5\times77=385\). Hence, 385 is the correct option. Choosing 365 would result from using an incorrect number of terms or last term. Exam tip: identify \(a\), \(d\), \(n\), and the last term before applying the sum formula.

Related tags

Arithmetic ProgressionSum Of TermsAp FormulaClass 10 MathematicsNth TermFinding The Sum Of The First $N$ Terms Of An ApFinding The Sum Of The First N Terms Of An ApArithmetic Progressions (Ap)
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10 more MCQs
  1. 1If an arithmetic progression has first term \(a\), common difference \(d\), and \(n\) terms, which formula correctly represents the sum of its first \(n\) terms?
  2. 2Find the sum of the first (15) terms of the AP (4,8,12,\ldots).
  3. 3Which formula correctly represents the sum of the first \(n\) terms of an AP with first term \(a\) and common difference \(d\)?
  4. 4What is the sum of the first (25) terms of the AP (1,3,5,\ldots)?
  5. 5What is the sum of the first (12) terms of the AP (10,20,30,\ldots)?
  6. 6If the first term of an AP is (5), the last term is (45), and the number of terms is (9), what is the sum?
  7. 7Find the sum of the first (30) terms of the AP (3,6,9,\ldots).
  8. 8What is the sum of the first (8) terms of the AP (20,18,16,\ldots)?
  9. 9If the AP is (9,13,17,\ldots), what is the sum of the first (11) terms?
  10. 10What is the sum of the first (14) terms of the AP (12,17,22,\ldots)?
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