Question

which term of the series -2,0,2,4,..........is 8o  and 102 ?

Answer 1

Hi ,

Let us see the given series :

-2 , 0 , 2 , 4 ,....

First term = a = - 2

a2 - a1 = 0 - ( - 2 ) = 2 -------(1)

a3 - a2 = 2 - 0 = 2 ------------(2)

( 1 ) = ( 2 )

Therefore

The series in arithmetic progression

Common difference = d = 2

Last term = an = l = a + ( n - 1 ) d

i) if l = 80 , a = -2 , d = 2 , n = ?

a + ( n - 1 ) d = l

-2 + ( n - 1 ) 2 = 80

( n - 1 ) 2 = 80 + 2

(n - 1 ) 2 = 82

n - 1 = 82 / 2

n - 1 = 41

n = 41 + 1

n = 42

Therefore 80 is 42nd term in an AP.

ii ) if l = 102 , a = -2 , d = 2 , n =?

-2 + ( n - 1 ) 2 = 102

( n - 1 ) 2 = 102 + 2

( n - 1 ) 2 = 104

n - 1 = 104 / 2

n - 1 = 52

n = 52 + 1

n = 53

Therefore

102 is the 53 rd term in an given A P.

I hope this will useful to u.

*****

Answer 2

Solution :-

Given Arithmetic Progression = -2, 0, 2, 4,.........

We have to find which term of the given A. P. is 80 and 102.

⇒ an = a + (n -1)d
Where a = -2
and common difference (d) = 0 - (-2)
= 0 + 2
= 2

Therefore,
80 = -2 + (n - 1)2
80 = -2 + 2n -2
80 + 2 + 2 = 2n
84 = 2n 
n = 84/2
n = 42

So, 80 is 42nd term of the given A.P. 

102 = -2 + (n - 1)2
102 = -2 + 2n -2
102 + 2 + 2 = 2n
106 = 2n
n = 106/2
n = 53

So, 102 is 53rd term of the given A.P.

Answer.