Question

The sum of 5th and 7th term of an



a.p.is 4 and the 10 th term is 46 .find the



a.p.

Answer 1

A5 = a + ( 5-1 ) *d = a + 4 d

A7 = a + ( 7-1 ) *d = a + 6 d

A10 = 46 = a + 9 d - - - - ( i )

ACCORDING TO THE QUESTION,

A5 + A7 = 4

( a + 4d ) + ( a + 6 d ) = 4

2a + 10 d = 4

2 ( a + 5 d ) = 4

a + 5d = 2 - - - ( ii )

Subtracting equation ( i ) and ( ii )

a + 9 d = 46
- a - 5d = - 2

=> 4d = 44

=> COMMON DIFFERENCE ( d ) = 11

Putting value of d in equation ( i )

a + 9 ( 11 ) = 46

a = 46 - 99

a = - 53

First term = a = - 53

Second term = a+d = - 53 + 11 = - 42

Third term = a+ 2d = - 53 + 2 ( 11 ) = - 53 + 22

= - 31

❇ AP = - 53, - 42, - 31............