Math, asked by karinakaria, 1 year ago

which term of the AP 40,36,32,.... is 0 ? the aum of how many terms of the AP is 0?

Answers

Answered by Steph0303
8

Answer:

AP = 40, 36, 32, ... 0

To find which term is 0.

Last term = 0

First term = 40

Common Difference = -4

Number of terms = ?

⇒ l = a + ( n - 1 ) d

⇒ 0 = 40 + ( n - 1 ) -4

⇒ 0 - 40 = ( n - 1 ) - 4

⇒ -40 = -4n + 4

⇒ -40 - 4 = -4n

⇒ -44 = -4n

⇒ 4n = 44

⇒ n = 44 / 4 = 11

Hence the 11th term of the AP is zero.

Also sum of n terms is given to be 0. We must find the value of n.

⇒ Sum of n terms = ( n / 2 ) ( 2a + ( n - 1 ) d )

⇒ 0 = ( n / 2 ) ( 2 ( 40 ) + ( n - 1 ) -4 )

⇒ 0 = ( n / 2 ) ( 80 - 4n + 4 )

⇒ 0 × 2 = n ( 84 - 4n )

⇒ 0 = n ( 84 - 4n )

⇒ 0 / n = ( 84 - 4n )

⇒ 0 = 84 - 4n

⇒ 4n = 84

⇒ n = 84 / 4 = 21

Hence the sum of first 21 terms is zero. Hence 21 terms must be added to get 0 as the sum.

This is the required answer.

Answered by Anonymous
8

Let the first term be a.

Let the common difference be d.

Given a=40

d=36-40=-4

Now,

Let the nth term be 0.

nth term=a+(n-1)d

Therefore

a+(n-1)d=0

=40+(-4)(n-1)=0

=40-4n+4=0

=-4n+44=0

=n=-44/-4

=11

Let n terms added be =0.

n/2*[2a+(n-1)d]=0

n*[2a+(n-1)d]=0

=n[2*40+(n-1)(-4)]=0

=n[80-4n+4]=0

=n[84-4n]=0

Either n=0 or 84-4n=0

But n cannot be zero.

So

84-4n=0

4n=84

n=84/4

=21

Answer:

11th  term is 0

21 terms have to be added to get 0.

Hope it helps you.

Have a nice day:-)



karinakaria: yessss!!!!
karinakaria: ok
Steph0303: Great answer :)
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