Consider the 8th term of the following Arithmetic Progression.
(A) 8, 3, −2...
(B) 7, 13, 19...
(C) 3, 8, 13...
(D) 11, 16, 21...
Arrange the 8th term of the above Arithmetic Progression in ascending order and choose the correct answer from the options given below.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A), (C), (D), (B)
In an arithmetic progression each term is the one before it plus a fixed common difference \(d\), so the \(n\)th term is \(a_n=a+(n-1)d\). The 8th term is \(a+7d\): the first term plus seven common differences.
(A) 8, 3, −2, ...: first term 8, common difference −5
\(a_8=8+7(-5)=-27\)
(B) 7, 13, 19, ...: first term 7, common difference 6
\(a_8=7+7\times6=49\)
(C) 3, 8, 13, ...: first term 3, common difference 5
\(a_8=3+7\times5=38\)
(D) 11, 16, 21, ...: first term 11, common difference 5
\(a_8=11+7\times5=46\)
In ascending order the 8th terms are \(-27\lt38\lt46\lt49\), that is (A), (C), (D), (B).