Advertisements
Advertisements
प्रश्न
A man saved Rs 66000 in 20 years. In each succeeding year after the first year he saved Rs 200 more than what he saved in the previous year. How much did he save in the first year?
Advertisements
उत्तर
Let Rs. x be saved in first year
Annual increment = Rs. 200
Which forms an A.P.
First term = a and common difference d = 200
n = 20 years
∴ Sn = `n/2[2a + (n - 1)d]`
⇒ S20 = `20/2 [2a + (20 - 1) 200]`
⇒ 66000 = 10[2a + 3800]
⇒ 6600 = 2a + 3800
⇒ 2a = 6600 – 3800
⇒ 2a = 2800
⇒ a = 1400
Hence, the man saved Rs. 1400 in the first year.
APPEARS IN
संबंधित प्रश्न
Find the sum of odd integers from 1 to 2001.
In an A.P, the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20th term is –112.
How many terms of the A.P. -6 , `-11/2` , -5... are needed to give the sum –25?
If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term
Sum of the first p, q and r terms of an A.P. are a, b and c, respectively.
Prove that `a/p (q - r) + b/q (r- p) + c/r (p - q) = 0`
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual installment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?
A man deposited Rs 10000 in a bank at the rate of 5% simple interest annually. Find the amount in 15th year since he deposited the amount and also calculate the total amount after 20 years.
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, ...
An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term.
How many numbers are there between 1 and 1000 which when divided by 7 leave remainder 4?
If the sum of three numbers in A.P. is 24 and their product is 440, find the numbers.
Find the sum of the following arithmetic progression :
50, 46, 42, ... to 10 terms
Find the sum of all integers between 84 and 719, which are multiples of 5.
Find the sum of all integers between 50 and 500 which are divisible by 7.
Solve:
25 + 22 + 19 + 16 + ... + x = 115
The sum of first 7 terms of an A.P. is 10 and that of next 7 terms is 17. Find the progression.
Show that x2 + xy + y2, z2 + zx + x2 and y2 + yz + z2 are consecutive terms of an A.P., if x, y and z are in A.P.
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?
Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalments of Rs 1000 plus 10% interest on the unpaid amount. How much the scooter will cost him.
Write the common difference of an A.P. whose nth term is xn + y.
The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be
If the sum of n terms of an A.P., is 3 n2 + 5 n then which of its terms is 164?
Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn − k Sn − 1 + Sn − 2 , then k =
Mark the correct alternative in the following question:
If in an A.P., the pth term is q and (p + q)th term is zero, then the qth term is
Write the quadratic equation the arithmetic and geometric means of whose roots are Aand G respectively.
If a, b, c are in A.P. and x, y, z are in G.P., then the value of xb − c yc − a za − b is
If for an arithmetic progression, 9 times nineth term is equal to 13 times thirteenth term, then value of twenty second term is ____________.
The product of three numbers in A.P. is 224, and the largest number is 7 times the smallest. Find the numbers
If a1, a2, ..., an are in A.P. with common difference d (where d ≠ 0); then the sum of the series sin d (cosec a1 cosec a2 + cosec a2 cosec a3 + ...+ cosec an–1 cosec an) is equal to cot a1 – cot an
Find the rth term of an A.P. sum of whose first n terms is 2n + 3n2
If the sum of p terms of an A.P. is q and the sum of q terms is p, show that the sum of p + q terms is – (p + q). Also, find the sum of first p – q terms (p > q).
If the sum of n terms of an A.P. is given by Sn = 3n + 2n2, then the common difference of the A.P. is ______.
If 9 times the 9th term of an A.P. is equal to 13 times the 13th term, then the 22nd term of the A.P. is ______.
If the sum of n terms of a sequence is quadratic expression then it always represents an A.P
If the ratio of the sum of n terms of two APs is 2n:(n + 1), then the ratio of their 8th terms is ______.
If n AM's are inserted between 1 and 31 and ratio of 7th and (n – 1)th A.M. is 5:9, then n equals ______.
If a1, a2, a3, .......... are an A.P. such that a1 + a5 + a10 + a15 + a20 + a24 = 225, then a1 + a2 + a3 + ...... + a23 + a24 is equal to ______.
