Question

The third and sixth term of an Ap are 14 and 29 respectively.find the common difference and nth term

Answer 1

To find the common difference, we can use the formula:

common difference = (nth term - first term) / (n - 1)

where n is the number of terms in the AP.

Let's find the first term using the third term and the common difference:

14 = a + 2d ....(1)

where a is the first term and d is the common difference.

Similarly, we can find the first term using the sixth term:

29 = a + 5d ....(2)

Now we can solve the two equations to find the values of a and d:

Subtracting (1) from (2) we have:
15 = 3d
d = 5

Substituting d = 5 in equation (1), we get:
a = 4

Therefore, the common difference is 5.

To find the nth term, we can use the formula:

nth term = a + (n-1)d

Substituting the values of a and d, we have:

nth term = 4 + 5(n-1)
nth term = 5n - 1

Therefore, the nth term of the AP is 5n - 1.