Question

Find the value of a such that 2a – 1, 7 and 3a are the three consecutive terms of A.P.

Answer 1

Hint: Let us find the difference between the first two terms and then find the difference between the next two terms of the given A.P by subtracting two consecutive terms. Then use the definition of common difference of A.P. and get the solution.

Complete step-by-step answer:
As we know that for any A.P, its common difference is the difference between its two consecutive terms.
As we know that if A, B and C are three terms in A.P then the common difference of the A.P will be B–A . And as we know that C is also a term of A.P. So, common differences can also be written asC–B.
So, B – A = C – B
Now, we are given with the three terms of A.P.
So, 7 – (2a – 1) = 3a – 7
Now we had to solve the above equation to get the value of a.
Adding 2a to both sides of the above equation we get,
7 + 1 = 5a – 7
Adding 7 to both sides of the above equation. We get,
8 + 7 = 5a
a = $\dfrac{{15}}{5}$ = 3
Hence, the correct value of a so, that the given three terms are consecutive terms of A.P will be 3.

Note: Whenever we come up with this type of problem then there is also another method to find the value of a. In other methods if A, B and C are the three consecutive terms of an A.P. then according to the condition for the second term of A.P we can write B as 2B = A + C, and then we will solve this equation to find the correct value of a.