Question

Hey friends please help me solve this..Q. the fifth term of an AP exceed twice the second term by 1. The tenth term exceed the fourth term by 3. Find the first term and the common difference.

Answer 1

Let the first term be a.

Let the common difference be d.

nth term is a+(n-1)d

5th term is a+(5-1)d

==>a+4d

2nd term is a+d

fifth term exceed twice the second by 1

==>a+4d=2(a+d)+1

==>a+4d=2a+2d+1

==>a+2d+1=0...........................(1)

tenth term is a+9d

fourth term is a+3d

a+9d=a+3d+3

==> 6d=3

==>d=3/6

==>d=1/2

Putting this value of d in 1 we get:

==>a+2d+1=0

==>a+2*1/2+1=0

==>a+2=0

==>a=-2

Hence a=-2 and d=1/2

Hope it helps you.

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Answer 2

hello...

▶first term be a.

▶common difference be d.

▶nth term =a+(n-1)d

▶5th term=a+(5-1)d

=a+4d

▶2nd term is a+d

▶5th term exceed twice the second by 1
so...

=a+4d=2(a+d)+1

=a+4d=2a+2d+1

=a+2d+1=0....................................[1]

▶▶10th term =a+9d

▶▶4th term =a+3d

▶a+9d=a+3d+3

= 6d=3

=d=3/6

=d=1/2

▶▶▶▶▶From 1◀◀◀◀◀◀

=a+2d+1=0

=a+2*1/2+1=0

=a+2=0

or....

=a=-2

so therefore...

a=-2 and d=1/2

thankyou...