Question

the
29. A person writes a letter to four of his friends. He asks each one of them to copy
the letter and mail to four different persons with instruction that they move
chain similarly. Assuming that the chain is not broken and that it costs 50 paise to
mail one letter. Find the amount spent on the postage when 8th set of letter is
mailed.
annually.
​

Answer 1

According to question , one person writes letter to his 4 friends

Now, each of these 4 friends will write letter to their 4 friends . So, the number of letters written here will be 4  

2

 

This continues....

So, the number of letters written forms a G.P. 4,4  

2

,4  

3

,....4  

8

 

Here, a=4,r=4,n=8

We know Sum of n terms of G.P. =  

r−1

a(r  

n

−1)

​  

 

So, sum of 8 terms of G.P. is  

4−1

4(4  

8

−1)

​  

=  

3

4(65536−1)

​  

 

=  

3

4×65535

​  

=87380

So, the number of letter written in 8 th set of letter is 87380.

Cost to mail one letter is 50paise  

So, cost to mail 87380 is Rs  

100

50

​  

×87380=Rs.43690