Question

2. The next two terms of the AP : k, 2k + 1,3k + 2, 4k + 3...................are (1)
a 5k + 4 and 6k + 5
b. 4k + 4 and 4k+ 5
c 5k +5 and 6k + 6
d. 5k and 6k​

Answer 1

Given:

An Arithmetic Progression k, 2k + 1, 3k + 2, 4k + 3, and so on.

To Find:

The next two terms in the A.P are?

Solution:

The given problem can be solved using the concepts of Arithmetic progression.

1. The given A.P series is k, 2k + 1, 3k + 2, 4k + 3.

2. The first term in the A.P is denoted by a,

=> a = k,

3. The common difference is calculated by subtracting any two consecutive terms. ( The first term among the two terms should be subtracted with the second term ). The Common difference is denoted by d.

=> d = 2k + 1 - k ,

=> d = k + 1,

4. The nth term of an A.P is given by the formula$T_{n}= a+ (n-1)d$.

=> Fifth term = T5 = a + 4d = k + 4k + 4 = 5k + 4,

=> Sixth term = T6 = a + 5d = k + 5k + 5 = 6k + 5.

5. Hence, the fifth and sixth terms are 5k + 4 and 6k + 5 respectively.

Therefore, Option A is the correct answer.