Question

The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 34. Find the first four terms and the 30th term of the AP.​

Answer 1

Answer:

A4=a+3d

A8=a+7d

By condition

A4+A8=24

a+3d+a+7d=24

2a+10d=24..................(I)

A6=a+5d

A10=a+9d

By condition

A6+A10=34

a+5d+a+9d=34

2a+14d=34...................(ii)

Eqn(2)-Eqn (1)

2a+14d=34

2a+10d=24

-. -. -

___________

4d=10

d=10/4

d=5/2(Put in eqn I)

2a+10(5/2)=24

2a+25=24

2a=24-25

2a=(-1)

a= (-1/2)

A2=a+d

= -1/2+5/2

=4/2

=2

A3=a+2d

= -1/2+2(5/2)

= -1/2+5

= -1+10/2

=9/2

A4=a+3d

= -1/2+3(5/2)

= -1/2+15/2

= -1+15/2

=14/2

=7

A30=a+29d

= -1/2+29(5/2)

= -1/2+145/2

= -1+145/2

= 144/2

=72

Hope it helps you mate my hands were literally paining while typing it.Block A terms here refer to the term of AP