Advertisements
Advertisements
प्रश्न
Find the sum \[7 + 10\frac{1}{2} + 14 + . . . + 84\]
Advertisements
उत्तर
(v) \[7 + 10\frac{1}{2} + 14 + . . . + 84\]
Common difference of the A.P is
(d) =
`=10 1/2-7`
`=21/2 - 7`
`=(21-14)/2`
`=7/2`
So here,
First term (a) = 7
Last term (l) = 84
Common difference (d) = `7/2`
So, here the first step is to find the total number of terms. Let us take the number of terms as n.
Now, as we know,
`a_n = a + (n-1) d`
So, for the last term,
`84 = 7 + (n-1) 7/2`
`84 = 7 + (7n)/2 - 7/2`
`84 = (14-7)/2 + (7n)/2`
84 (2) = 7 + 7n
Further solving for n,
7n = 168 - 7
`n = 161/7`
n = 23
Now, using the formula for the sum of n terms, we get
`S_n = 23/2 [2(7) + (23-1) 7/2]`
` = 23/2 [14+(22)7/2]`
`=23/2(14+77) `
`= 23/2 (91)`
On further simplification, we get,
`S_n = 2093/2`
Therefore, the sum of the A.P is `S_n = 2093/2`
APPEARS IN
संबंधित प्रश्न
In an AP: Given a = 5, d = 3, an = 50, find n and Sn.
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 first 40 positive integers divisible by 6.
A contract on a construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs. 200 for the first day, Rs. 250 for the second day, Rs. 300 for the third day, etc., the penalty for each succeeding day being Rs. 50 more than for the preceding day. How much money does the contractor have to pay as a penalty if he has delayed the work by 30 days.
If the pth term of an A. P. is `1/q` and qth term is `1/p`, prove that the sum of first pq terms of the A. P. is `((pq+1)/2)`.
Show that `(a-b)^2 , (a^2 + b^2 ) and ( a^2+ b^2) ` are in AP.
What is the sum of first n terms of the AP a, 3a, 5a, …..
The next term of the A.P. \[\sqrt{7}, \sqrt{28}, \sqrt{63}\] is ______.
Find the first term and common difference for the following A.P.:
5, 1, –3, –7, ...
If the 9th term of an A.P. is zero then show that the 29th term is twice the 19th term?
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.
Q.10
The sum of first n terms of an A.P. whose first term is 8 and the common difference is 20 equal to the sum of first 2n terms of another A.P. whose first term is – 30 and the common difference is 8. Find n.
What is the sum of an odd numbers between 1 to 50?
The famous mathematician associated with finding the sum of the first 100 natural numbers is ______.
Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.
[Hint (iii) : These numbers will be : multiples of 2 + multiples of 5 – multiples of 2 as well as of 5]
If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is ______.
Kanika was given her pocket money on Jan 1st, 2008. She puts Rs 1 on Day 1, Rs 2 on Day 2, Rs 3 on Day 3, and continued doing so till the end of the month, from this money into her piggy bank. She also spent Rs 204 of her pocket money, and found that at the end of the month she still had Rs 100 with her. How much was her pocket money for the month?
Three numbers in A.P. have the sum of 30. What is its middle term?
