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Class 10MathematicsArithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APExpertLevel 69
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If the sum of the first n terms of an arithmetic progression is S_n = 6n² − 5n, what is the 18th term?

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Answer and explanation

Correct answer: 205

The correct answer is C, 205. For any sequence, the nth term can be obtained from consecutive partial sums: a_n = S_n − S_(n−1). Here, S_18 = 6(18²) − 5(18) = 6(324) − 90 = 1944 − 90 = 1854. Similarly, S_17 = 6(17²) − 5(17) = 6(289) − 85 = 1734 − 85 = 1649. Therefore a_18 = S_18 − S_17 = 1854 − 1649 = 205. The other options result from arithmetic or substitution errors, such as using the wrong preceding sum or mishandling the negative linear term.

Related tags

Arithmetic ProgressionPartial SumsNth TermFinding The Sum Of The First $N$ Terms Of An ApFinding The Sum Of The First N Terms Of An ApArithmetic Progressions (Ap)Arithmetic Progressions ApMathematics

Frequently asked questions

What is the correct answer to this question?

205

Why is this the correct answer?

The correct answer is C, 205. For any sequence, the nth term can be obtained from consecutive partial sums: a_n = S_n − S_(n−1). Here, S_18 = 6(18²) − 5(18) = 6(324) − 90 = 1944 − 90 = 1854. Similarly, S_17 = 6(17²) − 5(17) = 6(289) − 85 = 1734 − 85 = 1649. Therefore a_18 = S_18 − S_17 = 1854 − 1649 = 205. The other options result from arithmetic or substitution errors, such as using the wrong preceding sum or mishandling the negative linear term.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an 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. 6What will be the sum of the first (10) terms of the AP (7,14,21,\ldots)?
  7. 7If the first term of an AP is (5), the last term is (45), and the number of terms is (9), what is the sum?
  8. 8Find the sum of the first (30) terms of the AP (3,6,9,\ldots).
  9. 9What is the sum of the first (8) terms of the AP (20,18,16,\ldots)?
  10. 10If the AP is (9,13,17,\ldots), what is the sum of the first (11) terms?
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