Consider the 15th term of the following Arithmetic Progression (AP).
A. 2, 7, 12, ...
B. 10, 7, 4, ...
C. 3, 8, 13, ..., 253
D. 1, −1, −3, −5, ...
Arrange the 15th term of the above APs in ascending order.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → B, D, A, C
The \(n\)th term of an AP is \(a_{n}=a+(n-1)d\), where \(a\) is the first term and \(d\) the common difference. For the 15th term, \(a_{15}=a+14d\).
AP (A) starts at 2 and rises by 5: \(a_{15}=2+70=72\)
AP (B) starts at 10 and falls by 3: \(a_{15}=10-42=-32\)
AP (C) starts at 3 and rises by 5: \(a_{15}=3+70=73\) (the last term 253 does not change the 15th term)
AP (D) starts at 1 and falls by 2: \(a_{15}=1-28=-27\)
In ascending order: B (−32), D (−27), A (72), C (73).