1.

In an AP, if the third term and seventh term are 4 and 8 respectively, then find which term value is zero.

Answer»

Given:-

In an AP, if the third term and seventh term are 4 and 8 respectively.

To find:-

Find which term value is zero ?

Third term of the given AP = 4

t3 = 4

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

Seventh term of the given AP = 8

t7 = 8

a + 6d = 8 ------(2)

On solving (1) & (2)

a + 2d = 4

a + 6d = 8

(-)

_________

0 - 4d = -4

_________

=> -4d = -4

=> 4d = 4

=> d = 4/4

=> d = 1

Common difference of the AP = 1

On Substituting the value of d in (1)

=> a+2(1) = 4

=> a+2 = 4

=>a = 4-2

=> a = 2

First term of the AP = 2

Then the AP :2,3,4,5,6,7,8....

Let nth term of the AP will be zero

=> tn = 0

=> a+(n-1)d = 0 

=> 2+(n-1)(1) = 0

=> 2+(n-1) = 0

=> 2+n-1 = 0

=> n+1 = 0

=> n = -1

Number of terms = -1

n = -1 , but n can not be negative

So there is no such term in the given AP can not be equal to zero.

And also It is an increasing series (AP)


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