Question

State true or false for any arithmetic progression, when a fixed number is added or subtracted to each term, the resulting sequence still remains an A.P. with the common difference remaining unchanged.
A. True
B. False

Answer 1

Hint:The question is related to arithmetic progression. The first term of the A.P is called a term and the difference between the second term and the first term is mentioned by letter d. In A.P the last term is denoted by ${a_n}$.Using this definition we try to solve the question.

Complete step-by-step answer:
When we multiply, divide, subtract or add any terms in a general arithmetic progression then the resulting sequence is also an A.P and also the common difference remains same in between any two terms in A.P.
We can understand this by an example
Let A.P
$2,4,6,8,.........,64$
Here a = 2 and d = 4 – 2 = 2
If we add 2 in every term in A.P
$2 + 2,4 + 2,6 + 2,8 + 2,.........,64 + 2$
We get a new A.P
$4,6,8,10,..........,66$
Here a =4 and d =6 – 8= 2
We can see that the d in both A.P is same
Now If we subtract 2 in every term in A.P
$2 - 2,4 - 2,6 - 2,8 - 2,.........,64 - 2$
We get new A,P
$0,2,4,6,..........,62$
Here a =0 and d =2 – 0= 2
We can see that the d in both A.P is same
Hence we can say that when a fixed number is added or subtracted to each term, the resulting sequence still remains an A.P. with the common difference remaining unchanged.

So, the correct answer is “Option A”.

Note:For solving this question you must know the properties and identities of A.P. An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. In A.P last term is denoted by ${a_n}$ and we can find ${a_n}$ by using the formula ${a_n} = a + (n - 1)d$,where a is the first term of A.P, n is the number of terms and d is a common difference.