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
RELATED QUESTIONS
Find the sum of first 8 multiples of 3
Find the sum of the following arithmetic progressions:
`(x - y)/(x + y),(3x - 2y)/(x + y), (5x - 3y)/(x + y)`, .....to n terms
Find the sum of the first 40 positive integers divisible by 5
The 19th term of an AP is equal to 3 times its 6th term. If its 9th term is 19, find the AP.
How many terms of the AP 21, 18, 15, … must be added to get the sum 0?
Write an A.P. whose first term is a and common difference is d in the following.
a = –1.25, d = 3
If the common differences of an A.P. is 3, then a20 − a15 is
Write the value of a30 − a10 for the A.P. 4, 9, 14, 19, ....
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
How many terms of the A.P. 27, 24, 21, …, should be taken so that their sum is zero?
