In the sequence (1, 4, 9, 16, …), what will be the value of a_11 + a_12?
Answer and explanation
Correct answer: 265
The governing concept is recognizing the square-number sequence. The terms are 1², 2², 3², 4², and so on, so its general rule is a_n = n². Therefore a_11 = 11² = 121 and a_12 = 12² = 144. Adding these required terms gives a_11 + a_12 = 121 + 144 = 265. Hence option C is correct. The nearby choices can arise from squaring only one position, using the wrong position, or making an addition error. It is important not to interpret a_11 + a_12 as the term with index 23; it means the values of the 11th and 12th terms must be calculated separately and then added.
Frequently asked questions
What is the correct answer to this question?
265
Why is this the correct answer?
The governing concept is recognizing the square-number sequence. The terms are 1², 2², 3², 4², and so on, so its general rule is a_n = n². Therefore a_11 = 11² = 121 and a_12 = 12² = 144. Adding these required terms gives a_11 + a_12 = 121 + 144 = 265. Hence option C is correct. The nearby choices can arise from squaring only one position, using the wrong position, or making an addition error. It is important not to interpret a_11 + a_12 as the term with index 23; it means the values of the 11th and 12th terms must be calculated separately and then added.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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