Advertisements
Advertisements
प्रश्न
Find the sum of all odd natural numbers less than 50.
Advertisements
उत्तर
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
संबंधित प्रश्न
Determine the A.P. whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
Find the sum of the following arithmetic progressions: 50, 46, 42, ... to 10 terms
In an A.P. the first term is 25, nth term is –17 and the sum of n terms is 132. Find n and the common difference.
If 10 times the 10th term of an AP is equal to 15 times the 15th term, show that its 25th term is zero.
Kargil’s temperature was recorded in a week from Monday to Saturday. All readings were in A.P. The sum of temperatures of Monday and Saturday was 5°C more than sum of temperatures of Tuesday and Saturday. If temperature of Wednesday was –30° celsius then find the temperature on the other five days.
If the sum of P terms of an A.P. is q and the sum of q terms is p, then the sum of p + q terms will be
The common difference of the A.P. \[\frac{1}{3}, \frac{1 - 3b}{3}, \frac{1 - 6b}{3}, ...\] is ______.
Suppose three parts of 207 are (a − d), a , (a + d) such that , (a + d) >a > (a − d).
If an = 3 – 4n, show that a1, a2, a3,... form an AP. Also find S20.
The middle most term(s) of the AP: -11, -7, -3,.... 49 is ______.
