Question

The 5th & 13th term of an A.P are 5 and -3.Find the A.P and 16th term of the A.P.

Answer 1

A5=5
a+4d=5
a+12d=-3
...................
-8d=8
d=-1
a=9
A16=a+15d
=9-15
=-6
A.P=9,3,-3....

Answer 2

Hey Mate !

Here is your solution :

Let the first term is 'a' and common difference is 'd'.

First term = a

Common difference = d

5th term = 5

13th term = -3

A.P = ?

16th term = ?

Using formula :

=> nth term = First term + ( n - 1 ) Common difference


=> 5th tern = a + ( 5 - 1 )d

=> 5 = a + 4d

=> 5 - 4d = a ------------ ( 1 )

Again,

=> nth term = First term + ( n - 1 ) Common difference

=> 13th term = a + ( 13 - 1 )d

=> -3 = a + 12d

=> -3 - 12d = a ------------- ( 2 )

From ( 1 ) and ( 2 ) , we get ,

=> -3 -12d = 5 - 4d

=> -3 -5 = -4d + 12d

=> -8 = 8d

=> d = ( -8 ) ÷ 8

=> d = -1

By putting the value of 'd' in ( 1 ),

=> 5 - 4d = a

=> 5 -4( -1 ) = a

=> 5 + 4 = a

=> a = 9

Hence , first term = a = 9

Common difference = d = ( -1 )

Therefore ,

A.P = 9 , ( 9 - 1 ) , ( 9 - 1 - 1 ) , ( 9 - 1 - 1 - 1 ) .....

= 9 , 8 , 7 , 6 , 5 ..............

Using formula :

=> nth term = First term + ( n - 1 ) Common difference

=> 16th term = 9 + ( 16 - 1 ) ( -1 )

=> 16th term = 9 + ( 15 ) ( -1 )

=> 16th term = 9 - 15

=> 16th term = -6

Hence,

A.P. = 9,8,7,6,5 ............

16th term = ( -6 )


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Hope it helps !! ^_^