The (14)th term of an AP is (92) and (d=7). What is (a_1)?
Answer and explanation
Correct answer: \(1\)
For an AP, \(a_n=a_1+(n-1)d\). Thus, \(92=a_1+(14-1)\times7=a_1+91\), so \(a_1=1\). Option \(85\) would result from subtracting \(d\) only once, but moving from the 14th term to the first term requires subtracting \(13d\). Exam tip: always use \(n-1\) in the formula for the \(n\)th term.
Frequently asked questions
What is the correct answer to this question?
\(1\)
Why is this the correct answer?
For an AP, \(a_n=a_1+(n-1)d\). Thus, \(92=a_1+(14-1)\times7=a_1+91\), so \(a_1=1\). Option \(85\) would result from subtracting \(d\) only once, but moving from the 14th term to the first term requires subtracting \(13d\). Exam tip: always use \(n-1\) in the formula for the \(n\)th term.
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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