Advertisements
Advertisements
प्रश्न
First term and the common differences of an A.P. are 6 and 3 respectively; find S27.
Solution: First term = a = 6, common difference = d = 3, S27 = ?
Sn = `"n"/2 [square + ("n" - 1)"d"]` - Formula
Sn = `27/2 [12 + (27 - 1)square]`
= `27/2 xx square`
= 27 × 45
S27 = `square`
Advertisements
उत्तर
It is given that,
First term (a) = 6
Common difference (d) = 3
Sn = `n/2 [bb(2a) + (n - 1)d]` - Formula
∴ S27 = `27/2 [2(6) + (27 - 1)bb((3))]`
= `27/2 (12 + 26 (3))`
= `27/2 (12 + 78)`
= `27/2 xx bb90`
= 1215
Hence, S27 = 1215.
संबंधित प्रश्न
Find the sum given below:
34 + 32 + 30 + ... + 10
In an AP, given a = 2, d = 8, and Sn = 90, find n and an.
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?
Find the sum of the following arithmetic progressions:
41, 36, 31, ... to 12 terms
The sum of n natural numbers is 5n2 + 4n. Find its 8th term.
The 9th term of an AP is –32 and the sum of its 11th and 13th terms is –94. Find the common difference of the AP.
The sum of three numbers in AP is 3 and their product is –35. Find the numbers.
The sum of three consecutive terms of an AP is 21 and the sum of the squares of these terms is 165. Find these terms.
If the numbers a, 9, b, 25 from an AP, find a and b.
Rs 1000 is invested at 10 percent simple interest. Check at the end of every year if the total interest amount is in A.P. If this is an A.P. then find interest amount after 20 years. For this complete the following activity.
For what value of n, the nth terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... equal?
For what value of p are 2p + 1, 13, 5p – 3 are three consecutive terms of an A.P.?
Q.7
Q.14
If an = 3 – 4n, show that a1, a2, a3,... form an AP. Also find S20.
The famous mathematician associated with finding the sum of the first 100 natural numbers is ______.
The first term of an AP is –5 and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms and the common difference.
Complete the following activity to find the 19th term of an A.P. 7, 13, 19, 25, ........ :
Activity:
Given A.P. : 7, 13, 19, 25, ..........
Here first term a = 7; t19 = ?
tn + a + `(square)`d .........(formula)
∴ t19 = 7 + (19 – 1) `square`
∴ t19 = 7 + `square`
∴ t19 = `square`
An Arithmetic Progression (A.P.) has 3 as its first term. The sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference of the A.P.
The nth term of an A.P. is 6n + 4. The sum of its first 2 terms is ______.
