If the 2nd and 10th terms of an Arithmetic Progression (AP) are 6 and −10 respectively, which term of this AP is zero?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 5th
The \(n\)th term of an AP is \(a+(n-1)d\), where \(a\) is the first term and \(d\) the common difference. The two given terms give two equations; subtracting them removes \(a\).
The two given terms:
2nd term: \(a+d=6\) (1)
10th term: \(a+9d=-10\) (2)
Subtracting (1) from (2) (the \(a\) terms cancel):
Common difference: \(8d=-16\), so \(d=-2\)
First term, from (1): \(a=6-(-2)=8\)
The zero term:
Setting the \(n\)th term equal to zero: \(8+(n-1)(-2)=0\)
\(n-1=4\), so \(n=5\): the 5th term is zero (8, 6, 4, 2, 0)