Question

The 7th term of A.p is 32 and 13th term is 62 find rhe ap

Answer 1

Let first term = a

common difference = d

nth term = a + (n-1 )d

7th term = a + 6d = 32 ........(1)

13th term = a + 12d = 62 .........(2)

eq.(2) - ( 1)

( a + 12d ) - ( a + 6d ) = 62 - 32

a + 12d - a - 6d = 30

6d = 30

d = 30/6 = 5

Put d in eq. ( 1 )

a + 6 x 5 = 32

a + 30 = 32

a = 2

A.P. = 2 , 7, 12 , 17, ........

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Answer 2

a7= a+6d = 32
a13= a + 12d = 62

a + 6d = 32 .............1 equation
a + 12d = 62.............2 equation

Subtract equation 1 and 2 ; we get
a-a + 6d- 12d = 32-62
0 -6d = - 30
6d = 30
d =5put d= 5 in equation 1
a+ 6*5 =32
a= 32-30
a = 2

A.P. ------ 2;7;13 ; 18;23