Advertisements
Advertisements
प्रश्न
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 the 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.
Advertisements
उत्तर
The first person writes four letters. The 4 people who receive the letter then write four letters each. In this way, the chain keeps increasing.
Numbers of letters on each occasion up to 4, 16, 24, …… to 8 terms
Total number of papers = 4 + 16 + 64 + …… to 8 terms
= `(4(4^8 - 1))/(4 - 1)`
= `4/3 (65536 - 1)`
= `4/3 xx 65535`
= 87380
Postage cost of one letter = 50 paise = `1/2` Rs.
total postage cost = `87380 xx 1/2`
= 43690 Rs.
APPEARS IN
संबंधित प्रश्न
The sums of n terms of two arithmetic progressions are in the ratio 5n + 4: 9n + 6. Find the ratio of their 18th terms
Show that the sum of (m + n)th and (m – n)th terms of an A.P. is equal to twice the mth term.
Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respectively, show that S3 = 3 (S2– S1)
Let < an > be a sequence. Write the first five term in the following:
a1 = 1, an = an − 1 + 2, n ≥ 2
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
−1, 1/4, 3/2, 11/4, ...
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
9, 7, 5, 3, ...
Which term of the A.P. 3, 8, 13, ... is 248?
How many terms are there in the A.P. 7, 10, 13, ... 43 ?
How many terms are there in the A.P.\[- 1, - \frac{5}{6}, -\frac{2}{3}, - \frac{1}{2}, . . . , \frac{10}{3}?\]
If 9th term of an A.P. is zero, prove that its 29th term is double the 19th term.
The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term.
If < an > is an A.P. such that \[\frac{a_4}{a_7} = \frac{2}{3}, \text { find }\frac{a_6}{a_8}\].
The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceeds the second term by 6, find three terms.
Find the sum of the following arithmetic progression :
50, 46, 42, ... to 10 terms
Find the sum of the following arithmetic progression :
3, 9/2, 6, 15/2, ... to 25 terms
Find the sum of the following serie:
2 + 5 + 8 + ... + 182
Find the sum of the following serie:
101 + 99 + 97 + ... + 47
Find the sum of first n natural numbers.
Find the sum of all natural numbers between 1 and 100, which are divisible by 2 or 5.
Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder 7.
If 12th term of an A.P. is −13 and the sum of the first four terms is 24, what is the sum of first 10 terms?
If a, b, c is in A.P., then show that:
b + c − a, c + a − b, a + b − c are in A.P.
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
A man arranges to pay off a debt of Rs 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one-third of the debt unpaid, find the value of the first instalment.
A piece of equipment cost a certain factory Rs 600,000. If it depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?
A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much the tractor cost him?
A carpenter was hired to build 192 window frames. The first day he made five frames and each day thereafter he made two more frames than he made the day before. How many days did it take him to finish the job?
A man is employed to count Rs 10710. He counts at the rate of Rs 180 per minute for half an hour. After this he counts at the rate of Rs 3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.
Write the common difference of an A.P. the sum of whose first n terms is
Write the value of n for which n th terms of the A.P.s 3, 10, 17, ... and 63, 65, 67, .... are equal.
If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are
Mark the correct alternative in the following question:
The 10th common term between the A.P.s 3, 7, 11, 15, ... and 1, 6, 11, 16, ... is
Write the quadratic equation the arithmetic and geometric means of whose roots are Aand G respectively.
The first three of four given numbers are in G.P. and their last three are in A.P. with common difference 6. If first and fourth numbers are equal, then the first number is
The first term of an A.P. is a, the second term is b and the last term is c. Show that the sum of the A.P. is `((b + c - 2a)(c + a))/(2(b - a))`.
If there are (2n + 1) terms in an A.P., then prove that the ratio of the sum of odd terms and the sum of even terms is (n + 1) : n
In an A.P. the pth term is q and the (p + q)th term is 0. Then the qth term is ______.
The first term of an A.P.is a, and the sum of the first p terms is zero, show that the sum of its next q terms is `(-a(p + q)q)/(p - 1)`
The internal angles of a convex polygon are in A.P. The smallest angle is 120° and the common difference is 5°. The number to sides of the polygon is ______.
