The 10th term of an AP is 62 and d=5. What is a1?
Answer and explanation
Correct answer: 17
For an arithmetic progression, the difference between consecutive terms is constant. Its nth term is given by \\(a_n=a_1+(n-1)d\\), where \\(a_1\\) is the first term and \\(d\\) is the common difference. Here the tenth term is 62 and the common difference is 5, so the formula can be used to work backward to the first term.
Substitute the known values: \\(62=a_1+(10-1)5\\). Since \\(10-1=9\\), the added part is \\(9\\times5=45\\). Therefore \\(62=a_1+45\\), and subtracting 45 from both sides gives \\(a_1=62-45=17\\). Thus option D is correct. The result also makes sense because moving from the first term to the tenth term requires nine equal increases of 5, whose total increase is 45.
Frequently asked questions
What is the correct answer to this question?
17
Why is this the correct answer?
For an arithmetic progression, the difference between consecutive terms is constant. Its nth term is given by \\(a_n=a_1+(n-1)d\\), where \\(a_1\\) is the first term and \\(d\\) is the common difference. Here the tenth term is 62 and the common difference is 5, so the formula can be used to work backward to the first term.
Substitute the known values: \\(62=a_1+(10-1)5\\). Since \\(10-1=9\\), the added part is \\(9\\times5=45\\). Therefore \\(62=a_1+45\\), and subtracting 45 from both sides gives \\(a_1=62-45=17\\). Thus option D is correct. The result also makes sense because moving from the first term to the tenth term requires nine equal increases of 5, whose total increase is 45.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
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