Advertisements
Advertisements
Question
Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000?
Advertisements
Solution
Given that,
Yasmeen, during the first month, saves = Rs 32
During the second month, saves = Rs 36
During the third month, saves = Rs 40
Let Yasmeen saves Rs 2000 during the n months.
Here, we have arithmetic progression 32, 36, 40,...
First term (a) = 32,
Common difference (d) = 36 – 32 = 4
And she saves total money, i.e., Sn = Rs 2000
We know that, sum of first n terms of an AP is,
Sn = `n/2[2a + (n - 1)d]`
⇒ 2000 = `n/2[2 xx 32 + (n - 1) xx 4]`
⇒ 2000 = n(32 + 2n – 2)
⇒ 2000 = n(30 + 2n)
⇒ 1000 = n(15 + n)
⇒ 1000 = 15n + n2
⇒ n2 + 15n – 1000 = 0
⇒ n2 + 40n – 25n – 1000 = 0
⇒ n(n + 40) – 25(n + 40) = 0
⇒ (n + 40)(n – 25) = 0
∴ n = 25 ...[∵ n ≠ – 40]
Since, months cannot be negative
Hence, in 25 months she will save Rs 2000.
APPEARS IN
RELATED QUESTIONS
The houses in a row numbered consecutively from 1 to 49. Show that there exists a value of x such that sum of numbers of houses preceding the house numbered x is equal to sum of the numbers of houses following x.
If the mth term of an A.P. is 1/n and the nth term is 1/m, show that the sum of mn terms is (mn + 1)
Show that a1, a2,..., an... form an AP where an is defined as below:
an = 9 − 5n
Also, find the sum of the first 15 terms.
If the sum of first m terms of an A.P. is the same as the sum of its first n terms, show that the sum of its first (m + n) terms is zero
How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40?
Find the sum of first n odd natural numbers
Find the sum of all multiples of 7 lying between 300 and 700.
Find the value of x for which the numbers (5x + 2), (4x - 1) and (x + 2) are in AP.
Find the sum of first n even natural numbers.
If (2p – 1), 7, 3p are in AP, find the value of p.
Find the A.P. whose fourth term is 9 and the sum of its sixth term and thirteenth term is 40.
A piece of equipment cost a certain factory Rs 60,000. 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?
For what value of p are 2p + 1, 13, 5p − 3 are three consecutive terms of an A.P.?
If Sn denote the sum of n terms of an A.P. with first term a and common difference dsuch that \[\frac{Sx}{Skx}\] is independent of x, then
Two A.P.'s have the same common difference. The first term of one of these is 8 and that of the other is 3. The difference between their 30th term is
The sum of the first three terms of an Arithmetic Progression (A.P.) is 42 and the product of the first and third term is 52. Find the first term and the common difference.
The sum of first 14 terms of an A.P. is 1050 and its 14th term is 140. Find the 20th term.
Find the sum of first 20 terms of an A.P. whose first term is 3 and the last term is 57.
In an A.P., the sum of its first n terms is 6n – n². Find is 25th term.
Find the middle term of the AP. 95, 86, 77, ........, – 247.
