What is the sum of the first (5) terms of the sequence (2,5,10,17,26,\ldots)?
Answer and explanation
Correct answer: (60)
The question asks for the sum of the first five terms, so the listed terms from the first through the fifth must all be included exactly once. They are 2, 5, 10, 17, and 26. This is not asking for the fifth term alone. One may notice that the terms follow the rule \(n^2+1\), but direct addition is the simplest method for the requested small number of terms.
Add the terms in order: \(2+5=7\), \(7+10=17\), \(17+17=34\), and \(34+26=60\). Therefore the sum is 60, so option D is correct. Omitting the first term would give an incorrect total, and stopping at the fourth term would give only 34. Every one of the five specified terms must be counted.
Frequently asked questions
What is the correct answer to this question?
(60)
Why is this the correct answer?
The question asks for the sum of the first five terms, so the listed terms from the first through the fifth must all be included exactly once. They are 2, 5, 10, 17, and 26. This is not asking for the fifth term alone. One may notice that the terms follow the rule \(n^2+1\), but direct addition is the simplest method for the requested small number of terms.
Add the terms in order: \(2+5=7\), \(7+10=17\), \(17+17=34\), and \(34+26=60\). Therefore the sum is 60, so option D is correct. Omitting the first term would give an incorrect total, and stopping at the fourth term would give only 34. Every one of the five specified terms must be counted.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sequences.
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