Advertisements
Advertisements
प्रश्न
Obtain the sum of the first 56 terms of an A.P. whose 18th and 39th terms are 52 and 148 respectively.
Advertisements
उत्तर
t18 = 52 and t39 = 148 S56 = ?
tn = a + (n-1)d
t18 = a +( 18 - 1) d
52 = a + 17 d ......(i)
t39 = a + (39 -1) d
∴ 148 = a + 38d ........(2)
Adding (1) and (2)
a + 17d = 52
a + 38d = 148
2a = 55d = 200 .......(3)
Sn = `n/2` [2a + (n - 1) d ]
S56 = `56/2` [2a + (56 -1) d]
= 28 [2a + 55d ]
= 28(200) [from eq (3)]
S56 = 5600
APPEARS IN
संबंधित प्रश्न
Find the 9th term from the end (towards the first term) of the A.P. 5, 9, 13, ...., 185
Find the sum given below:
34 + 32 + 30 + ... + 10
In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant will be the same as the class, in which they are studying, e.g., a section of class I will plant 1 tree, a section of class II will plant 2 trees, and so on till class XII. There are three sections of each class. How many trees will be planted by the students?
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 25 terms of an A.P. whose nth term is given by an = 7 − 3n
Which term of the AP `5/6, 1, 1 1/6, 1 1/3,` ... is 3?
If k, (2k - 1) and (2k + 1) are the three successive terms of an AP, find the value of k.
Find the first term and common difference for the A.P.
0.6, 0.9, 1.2,1.5,...
Sum of 1 to n natural numbers is 36, then find the value of n.
There are 37 terms in an A.P., the sum of three terms placed exactly at the middle is 225 and the sum of last three terms is 429. Write the A.P.
The first term of an A.P. is p and its common difference is q. Find its 10th term.
If the sum of first p term of an A.P. is ap2 + bp, find its common difference.
The number of terms of the A.P. 3, 7, 11, 15, ... to be taken so that the sum is 406 is
Q.12
Q.16
Find the sum of first 20 terms of an A.P. whose first term is 3 and the last term is 57.
Find the sum of first 1000 positive integers.
Activity :- Let 1 + 2 + 3 + ........ + 1000
Using formula for the sum of first n terms of an A.P.,
Sn = `square`
S1000 = `square/2 (1 + 1000)`
= 500 × 1001
= `square`
Therefore, Sum of the first 1000 positive integer is `square`
The sum of the first 15 multiples of 8 is ______.
Find the sum of the integers between 100 and 200 that are
- divisible by 9
- not divisible by 9
[Hint (ii) : These numbers will be : Total numbers – Total numbers divisible by 9]
Find the sum of those integers from 1 to 500 which are multiples of 2 as well as of 5.
