What will be the 12th term in the sequence (3, 5, 9, 15, 23, ...)?
Answer and explanation
Correct answer: 135
The governing idea is finding an explicit rule from a quadratic pattern. The successive differences are 2, 4, 6, and 8, whose second difference is constant at 2, so the nth term has the form n^2 + bn + c. Testing the displayed terms gives a_n = n^2 - n + 3: for n = 1, 2, 3, 4, 5 it gives 3, 5, 9, 15, 23 respectively. Substituting n = 12, a_12 = 12^2 - 12 + 3 = 144 - 12 + 3 = 135. Hence option B is correct. The nearby alternatives 132, 138, and 141 can arise from using an incorrect linear continuation or making an arithmetic error while substituting 12.
Frequently asked questions
What is the correct answer to this question?
135
Why is this the correct answer?
The governing idea is finding an explicit rule from a quadratic pattern. The successive differences are 2, 4, 6, and 8, whose second difference is constant at 2, so the nth term has the form n^2 + bn + c. Testing the displayed terms gives a_n = n^2 - n + 3: for n = 1, 2, 3, 4, 5 it gives 3, 5, 9, 15, 23 respectively. Substituting n = 12, a_12 = 12^2 - 12 + 3 = 144 - 12 + 3 = 135. Hence option B is correct. The nearby alternatives 132, 138, and 141 can arise from using an incorrect linear continuation or making an arithmetic error while substituting 12.
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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