Advertisements
Advertisements
प्रश्न
Find the sum of all 2 - digit natural numbers divisible by 4.
Advertisements
उत्तर
2-digit numbers divisible by 4 are 12, 16, 20, ..., 96
We can see it forms an AP as the common difference is 4 and the first term is 4.
To find the number of terms n,
we know that
an = a+ (n − 1) d
96 = 12 + (n − 1)4
84 = (n − 1)4
21 = n − 1
22 = n
Now,
First term (a) = 12
Number of terms (n) = 22
Common difference (d) = 4
Now, using the formula for the sum of n terms, we get
`S_22 = 22/2 {2(12) + (22 - 1)4}`
`S_22 = 11 {24 + 84}`
`S_22 = 1188`
Hence, the sum of 22 terms is 1188 which are divisible by 4.
APPEARS IN
संबंधित प्रश्न
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.
The sum of n, 2n, 3n terms of an A.P. are S1 , S2 , S3 respectively. Prove that S3 = 3(S2 – S1 )
Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.
Find the sum of the following arithmetic progressions:
41, 36, 31, ... to 12 terms
Determine the A.P. Whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
Divide 24 in three parts such that they are in AP and their product is 440.
The angles of quadrilateral are in whose AP common difference is 10° . Find the angles.
Find the first term and common difference for the A.P.
0.6, 0.9, 1.2,1.5,...
In an A.P. the 10th term is 46 sum of the 5th and 7th term is 52. Find the A.P.
In an A.P. the first term is – 5 and the last term is 45. If the sum of all numbers in the A.P. is 120, then how many terms are there? What is the common difference?
If first term of an A.P. is a, second term is b and last term is c, then show that sum of all terms is \[\frac{\left( a + c \right) \left( b + c - 2a \right)}{2\left( b - a \right)}\].
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 n terms of an A.P. is 3n2 + 5n, then 164 is its
Q.11
How many terms of the A.P. 24, 21, 18, … must be taken so that the sum is 78? Explain the double answer.
Shubhankar invested in a national savings certificate scheme. In the first year he invested ₹ 500, in the second year ₹ 700, in the third year ₹ 900 and so on. Find the total amount that he invested in 12 years
If the sum of first n terms of an AP is An + Bn² where A and B are constants. The common difference of AP will be ______.
Find the middle term of the AP. 95, 86, 77, ........, – 247.
Find the sum of first 20 terms of an A.P. whose nth term is given as an = 5 – 2n.
Read the following passage:
|
India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs. The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 16000 sets in 6th year and 22600 in 9th year. |
- In which year, the production is 29,200 sets?
- Find the production in the 8th year.
OR
Find the production in first 3 years. - Find the difference of the production in 7th year and 4th year.
