If the fourth term of (4,4+d,4+2d,4+3d) is (31), what is the second term?
Answer and explanation
Correct answer: (13)
The terms shown have the standard AP form: first term 4, second term \\(4+d\\), third term \\(4+2d\\), and fourth term \\(4+3d\\). If the fourth term is known, first use it to determine the common difference. Then substitute that difference into the expression for the second term.
The fourth term is 31, so \\(4+3d=31\\). Subtracting 4 gives \\(3d=27\\), and dividing by 3 gives \\(d=9\\). The second term is therefore \\(4+d=4+9=13\\). Hence choice B is correct. The value 31 is the fourth term, not the difference, and 15 would result from an incorrect placement of the multiplier on \\(d\\).
Frequently asked questions
What is the correct answer to this question?
(13)
Why is this the correct answer?
The terms shown have the standard AP form: first term 4, second term \\(4+d\\), third term \\(4+2d\\), and fourth term \\(4+3d\\). If the fourth term is known, first use it to determine the common difference. Then substitute that difference into the expression for the second term.
The fourth term is 31, so \\(4+3d=31\\). Subtracting 4 gives \\(3d=27\\), and dividing by 3 gives \\(d=9\\). The second term is therefore \\(4+d=4+9=13\\). Hence choice B is correct. The value 31 is the fourth term, not the difference, and 15 would result from an incorrect placement of the multiplier on \\(d\\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Introduction to APs and common difference..
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