In an A.p , the 1oth term is 68 and the 4th term is 26 .find common different

Answer 1

To find the common difference of an arithmetic progression (A.P.), we need to use the formula for the nth term of an A.P., which is given by:

an = a + (n - 1)d

Where:
an = nth term
a = first term
n = number of terms
d = common difference

We are given that the 10th term (a10) is 68, so we can plug this into the formula:

68 = a + (10 - 1)d

We are also given that the 4th term (a4) is 26, so we can plug this into the formula:

26 = a + (4 - 1)d

Now, we have a system of equations with two unknowns (a and d). We can solve the system to find the values of a and d.

From the equations above, we have:

68 = a + 9d ...(1)
26 = a + 3d ...(2)

To solve this system, we can subtract equation (2) from equation (1):

68 - 26 = (a + 9d) - (a + 3d)
42 = 6d
d = 42/6
d = 7

So, the common difference (d) of the arithmetic progression is 7.