Question

If the sum of 3rd and 4th term is 19 and sum of 5th and 7th term is 34 then write AP​

Answer 1

Answer:  The series is 2,5,8

Step-by-step explanation:

If the sum of 3rd and 4th term is 19 and sum of 5th and 7th term is 34 then write AP​

an=a+(n-1)d

Here,a3=a+(3-1)d

​=a+2d

a4=a+(4-1)d

=a+3d

Therefore,

​=a+2d+a+3d=19

=2a+5d=19        equation1

Here,a5=a+(5-1)d

​=a+4d

a7=a+(7-1)d

=a+6d

Therefore,

​=a+4d+a+6d=34

=2a+10d=34       equation2

Subtract equation1 from equation1

2a+10d=34  

-2a+5d=19

5d=15

d=3

Hence, we get the common difference is 3

Now we have to find the first term by substitutind common difference in equation 1 or 2

2a+10d=34  

2a+10x3=34  

2a+30=34  

2a=34-30

2a=4

a=2

Therefore,

a1=a=2

a2=a+d=2+3=5

a3=a+2d=2+(2x3)=8

Hence, we get the series 2,5,8