Question

the sum of 5th and 7th term of an ap is 52 and 10th term is 46 find common difference of the AP​

Answer 1

Answer:

The common difference of A.P. is 5.

Step-by-step explanation:

Given that-

The 10th term of A.P. = 46

The sum of 5th and 7th term = 46

common difference (d) = ?

Using formula-

nth term of A.P.-

$T_{n} = [a + (n - 1)d]$

Where a is first term of A.P.

d is common difference

n is number of term

So, $T_{5}  = [a + (5 - 1)d]$

$T_{5} = a + 4d$

Similarly, $T_{7} = [a + (7 - 1)d]$

$T_{7} = a + 6d$

But, $T_{5} + T_{7} = 52$

So, (a + 4d) + (a + 6d) = 52

2a + 10d = 52

Divided by 2 then-

a + 5d = 26                ------------------ 1.  

And, $T_{10} = [a +(10 - 1)d]$

But 10th term is 46.

So, 46 = a + 9d                  --------------------- 2.

Subtracting equation 1 from 2, we have-

(a + 9d) - (a + 5d) = 46 - 26

a + 9d - a - 5d = 20

4d = 20

d = 5

Hence, the common difference of A.P. is 5.