Question

the next 2 terms of AP 1/6,1/3,1/2 are respectively ​

Answer 1

Answer :2/3 and 5/6

Given :

1/6 , 1/3 , 1/2 are in the AP

To find :

Find the next two terms in the AP?

Solution :

Given that

1/6 , 1/3 , 1/2 are in the AP

First term=(t1) = 1/6

Second term = (t2) = 1/3

Common difference =

=> d= t2-t1

=> d = (1/3)-(1/6)

LCM of 3 and 6 = 6

=> d = (2-1)/6

=> d = 1/6

and

d = t3-t2

=>d = (1/2)-(1/3)

LCM of 2 and 3 = 6

=>d = (3-2)/6

=> d = 1/6

Next two terms are t4 and t5

We know that

tn = a+(n-1)d

t4 = a+(4-1)d

=> t4 = a+3d

=> t4 = (1/6)+3(1/6)

=> t4 = (1/6)+(3/6)

=> t4 = (1+3)/6

=> t4 = 4/6

=> t4= 2/3

and

t5 = a+(5-1)d

=> t5 = a+4d

=> t5 = (1/6)+4(1/6)

=> t5 = (1/6)+(4/6)

=> t5 = (1+4)/6

=> t5 = 5/6

Answer :-

The next two terms of the given AP are 2/3 and 5/6

Used formulae :

The General form of an AP is t1,t1+d,t1+2d,...

The General term of an AP = tn = a+(n-1)d