If the fifth term of the arithmetic progression (x, x + 9, x + 18, ...) is 58, what is x?
Answer and explanation
Correct answer: 22
The governing concept is the nth-term structure of an arithmetic progression. The displayed terms begin with a_1 = x and have common difference d = 9. Therefore the fifth term is a_5 = a_1 + (5 - 1)d = x + 4×9 = x + 36. Since this term is given as 58, solve x + 36 = 58, which gives x = 22. Thus option B is correct. Directly listing the terms gives x, x+9, x+18, x+27, x+36, so the same result is clear. Options 20, 24, and 26 would make the fifth term 56, 60, and 62 respectively, not 58.
Frequently asked questions
What is the correct answer to this question?
22
Why is this the correct answer?
The governing concept is the nth-term structure of an arithmetic progression. The displayed terms begin with a_1 = x and have common difference d = 9. Therefore the fifth term is a_5 = a_1 + (5 - 1)d = x + 4×9 = x + 36. Since this term is given as 58, solve x + 36 = 58, which gives x = 22. Thus option B is correct. Directly listing the terms gives x, x+9, x+18, x+27, x+36, so the same result is clear. Options 20, 24, and 26 would make the fifth term 56, 60, and 62 respectively, not 58.
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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