Advertisements
Advertisements
Question
Find the sum of all odd natural numbers less than 50.
Advertisements
Solution
Odd natural numbers less than 50 are as follows:
1, 3, 5, 7, 9, ........, 49
Now, 3 – 1 = 2, 5 – 3 = 2 and so on.
Thus, this forms an A.P. with first term a = 1,
Common difference d = 2 and last term l = 49
Now, l = a + (n – 1)d
`=>` 49 = 1 + (n – 1) × 2
`=>` 48 = (n – 1) × 2
`=>` 24 = n – 1
`=>` n = 25
Sum of first n terms = `S = n/2 [a + 1]`
`=>` Sum of odd natural numbers less than 50
= `25/2 [1 + 49]`
= `25/2 xx 50`
= 25 × 25
= 625
APPEARS IN
RELATED QUESTIONS
Find the sum given below:
`7 + 10 1/2 + 14 + ... + 84`
In an AP given d = 5, S9 = 75, find a and a9.
In an AP given l = 28, S = 144, and there are total 9 terms. Find a.
Find the sum of the first 40 positive integers divisible by 5.
Find the sum of the first 15 terms of the following sequences having nth term as an = 3 + 4n.
The 4th term of an AP is 11. The sum of the 5th and 7th terms of this AP is 34. Find its common difference.
The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by \[\frac{l^2 - a^2}{k - (l + a)}\] , then k =
If \[\frac{5 + 9 + 13 + . . . \text{ to n terms} }{7 + 9 + 11 + . . . \text{ to (n + 1) terms}} = \frac{17}{16},\] then n =
Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.
In a ‘Mahila Bachat Gat’, Kavita invested from the first day of month ₹ 20 on first day, ₹ 40 on second day and ₹ 60 on third day. If she saves like this, then what would be her total savings in the month of February 2020?
