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