What is the sum of the first 18 terms of the arithmetic progression 13, 17, 21, …?
Answer and explanation
Correct answer: 846
For an arithmetic progression, the sum of n terms is Sₙ = n/2[2a + (n−1)d], or equivalently n/2(a + l), where a is the first term and l is the last term. Here a = 13, d = 17 − 13 = 4, and n = 18. The eighteenth term is l = a + 17d = 13 + 17(4) = 81. Thus S₁₈ = 18/2(13 + 81) = 9 × 94 = 846. Therefore option A is correct. The other options do not follow from the correct last term or contain an arithmetic error in multiplying the average by the number of terms.
Frequently asked questions
What is the correct answer to this question?
846
Why is this the correct answer?
For an arithmetic progression, the sum of n terms is Sₙ = n/2[2a + (n−1)d], or equivalently n/2(a + l), where a is the first term and l is the last term. Here a = 13, d = 17 − 13 = 4, and n = 18. The eighteenth term is l = a + 17d = 13 + 17(4) = 81. Thus S₁₈ = 18/2(13 + 81) = 9 × 94 = 846. Therefore option A is correct. The other options do not follow from the correct last term or contain an arithmetic error in multiplying the average by the number of terms.
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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