What is the sum of the first 6 terms of the sequence (2, 5, 10, 17, 26, …)?
Answer and explanation
Correct answer: 97
The governing concept is obtaining and adding the required terms of a sequence. The pattern is n² + 1: for n = 1, 2, 3, 4, 5 it gives 2, 5, 10, 17, 26. Therefore the sixth term is 6² + 1 = 37. The first six terms are consequently 2, 5, 10, 17, 26, and 37. Adding them gives 2 + 5 + 10 + 17 + 26 + 37 = 97. Hence option C is correct. A quick check using the formula gives the same result: the sum of n² from 1 to 6 is 91, and adding 1 for each of the six terms gives 91 + 6 = 97. Options A, B, and D result from omitting or miscalculating a term.
Frequently asked questions
What is the correct answer to this question?
97
Why is this the correct answer?
The governing concept is obtaining and adding the required terms of a sequence. The pattern is n² + 1: for n = 1, 2, 3, 4, 5 it gives 2, 5, 10, 17, 26. Therefore the sixth term is 6² + 1 = 37. The first six terms are consequently 2, 5, 10, 17, 26, and 37. Adding them gives 2 + 5 + 10 + 17 + 26 + 37 = 97. Hence option C is correct. A quick check using the formula gives the same result: the sum of n² from 1 to 6 is 91, and adding 1 for each of the six terms gives 91 + 6 = 97. Options A, B, and D result from omitting or miscalculating a term.
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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