Question

In an A.P second term is 23 and tenth term is 63 , then the common difference is​

Answer 1

Answer:

a2=23

a+d=23

a10=63

a+9d=63

subtract both equation

-8d=-40

d=5

Answer 2

Answer:

5

Step-by-step explanation:

Given,

2nd term of an A.P(a_2) = 23

10th term of an A.P(a_10) = 63

To Find :-

Common difference(d)

How To Do :-

As they given the values of 2nd term and 10th term of A.P by using the formula of general term of an A.P we need to find those values in terms of first term(a) and common difference(d) and we need to subtract those two equations and we need to find the value of common difference(d).

Formula Required :-

nth term of an A.P

$a_n=a+(n-1)d$

Solution :-

2nd term of an A.P = 23

a_2 = 23

n = 2

Substituting in the formula :-

a + (2 - 1)d = 23

a + d = 23

[ Let it be equation - 1 ]

10th term of an A.P = 63

a_10 = 63

n = 10

Substituting in the formula :-

a + (10 - 1)d = 63

a + 9d = 63

[Let it be equation - 2]

Subtracting equation '1' from equation '2' :-

a + 9d - (a + d) = 63 - 23

a + 9d - a - d = 40

9d - d = 40

8d = 40

d = 40/8

d = 5

∴ Common difference(d) = 5