Question

If the 3rd and 9th term are A and -8respectively,which term of this A.P. is zero?

Answer 1

So fifth term will have AP 0    

Step-by-step explanation:

The AP is given by the formula for n terms

aₙ = a₁ + ( n-1) d

Now here it is given that d is the difference

For first

3rd term of AP is 4

Which means that n = 3 and aₙ=4

The formula is

aₙ = a₁ + ( n-1) d

Putting in the values

4 = a₁+ (3-1)d

a₁ + 2 d = 4               ................(i)

For second

9th term of AP is -8

Which means that n = 9 and aₙ=-8

The formula is

aₙ = a₁ + ( n-1) d

Putting in the values

-8 = a₁+ (9-1)d

a₁ + 8 d = -8               ................(ii)

Subtracting equation (i) from (ii) gives

(a₁ + 8 d) - (a₁ + 2 d)   = -8 - 4

It becomes

a₁+ 8 d - a₁ - 2 d = -12

6 d = -12

Dividing both sides by 6 gives

d = -2

Now for a₁ putting it in equation (i) which is

a₁ + 2d = 4

a₁ + 2(-2) = 4

a₁ - 4 = 4

adding 4 on both sides

a₁ - 4 + 4 = 4 + 4

a₁ = 8

Now to find which term of AP is 0

for this using

aₙ = a₁ + ( n-1) d

here

aₙ = 0, a₁ = 8 , d= -2 n =?

putting all values

0 = 8 + (n-1) * (- 2)

Subtracting -8 from both sides

0-8 = 8-8 + (n-1)*(-2)

-8 = (n-1)*(-2)

Dividing both sides by -2 we get

4 = n-1

adding 1 on both sides we get

n=5

So fifth term will have AP 0    

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