If (a_n=\frac{n(n+1)}{2}), what is the fourth term?
Answer and explanation
Correct answer: (10)
The formula gives the value of a term when its position number is known. For the fourth term, the position is represented by putting \\(n=4\\) into the given rule. The expression has a product in the numerator and division by 2, so both the multiplication and the division must be completed carefully. This type of formula is useful because it finds a term directly without listing all earlier terms.
Substitute 4: \\(a_4=\\frac{4(4+1)}{2}=\\frac{4\\times5}{2}=\\frac{20}{2}=10\\). Therefore, the fourth term is 10, so option D is correct. The value 6 would result from using an unsuitable expression, while 8 or 9 do not follow from the stated formula. The key step is to use the position number 4, not the term value from some other pattern.
Frequently asked questions
What is the correct answer to this question?
(10)
Why is this the correct answer?
The formula gives the value of a term when its position number is known. For the fourth term, the position is represented by putting \\(n=4\\) into the given rule. The expression has a product in the numerator and division by 2, so both the multiplication and the division must be completed carefully. This type of formula is useful because it finds a term directly without listing all earlier terms.
Substitute 4: \\(a_4=\\frac{4(4+1)}{2}=\\frac{4\\times5}{2}=\\frac{20}{2}=10\\). Therefore, the fourth term is 10, so option D is correct. The value 6 would result from using an unsuitable expression, while 8 or 9 do not follow from the stated formula. The key step is to use the position number 4, not the term value from some other pattern.
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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