What will be the tenth term of the sequence 1, 4, 7, 10, …?
Answer and explanation
Correct answer: 28
The governing concept is the nth term of an arithmetic sequence. The first term is a₁ = 1 and the common difference is d = 3. Therefore aₙ = a₁ + (n − 1)d = 1 + 3(n − 1) = 1 + 3n − 3 = 3n − 2. For the tenth term, put n = 10: a₁₀ = 3(10) − 2 = 30 − 2 = 28. Hence option C is correct. A direct continuation also gives the same value: the ninth term is 25 and adding 3 gives the tenth term 28. Option A is the ninth term, option B does not follow the constant difference, and option D forgets the subtraction of 2 in the general rule.
Frequently asked questions
What is the correct answer to this question?
28
Why is this the correct answer?
The governing concept is the nth term of an arithmetic sequence. The first term is a₁ = 1 and the common difference is d = 3. Therefore aₙ = a₁ + (n − 1)d = 1 + 3(n − 1) = 1 + 3n − 3 = 3n − 2. For the tenth term, put n = 10: a₁₀ = 3(10) − 2 = 30 − 2 = 28. Hence option C is correct. A direct continuation also gives the same value: the ninth term is 25 and adding 3 gives the tenth term 28. Option A is the ninth term, option B does not follow the constant difference, and option D forgets the subtraction of 2 in the general rule.
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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