What will be the (9)th term of the arithmetic progression (28,24,20,16,\ldots)?
Answer and explanation
Correct answer: (-4)
The governing concept is the nth-term formula for an arithmetic progression: a_n = a + (n − 1)d. Here the first term is a = 28 and the common difference is d = 24 − 28 = −4. For n = 9, a9 = 28 + (9 − 1)(−4) = 28 + 8(−4) = 28 − 32 = −4. Hence option A is correct. The negative answer is reasonable because the sequence decreases by 4 at every step: the terms are 28, 24, 20, 16, 12, 8, 4, 0, −4. Options B, C, and D result from using the wrong number of steps or stopping before the ninth term. The formula counts eight differences from the first to the ninth term.
Frequently asked questions
What is the correct answer to this question?
(-4)
Why is this the correct answer?
The governing concept is the nth-term formula for an arithmetic progression: a_n = a + (n − 1)d. Here the first term is a = 28 and the common difference is d = 24 − 28 = −4. For n = 9, a9 = 28 + (9 − 1)(−4) = 28 + 8(−4) = 28 − 32 = −4. Hence option A is correct. The negative answer is reasonable because the sequence decreases by 4 at every step: the terms are 28, 24, 20, 16, 12, 8, 4, 0, −4. Options B, C, and D result from using the wrong number of steps or stopping before the ninth term. The formula counts eight differences from the first to the ninth term.
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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