Advertisements
Advertisements
Question
Find the sum of the first 11 terms of the A.P : 2, 6, 10, 14, ...
Advertisements
Solution
In the given problem, we need to find the sum of terms for different arithmetic progressions. So, here we use the following formula for the sum of n terms of an A.P.,
`S_n = n/2[2a + (n - 1)d]`
Where; a = first term for the given A.P.
d = common difference of the given A.P.
n = number of terms
2, 6, 10, 14, ... to 11 terms
Common difference of the A.P. (d) = `a_2 - a_1`
= 6 - 2
= 4
Number of terms (n) = 11
The first term for the given A.P. (a) = 2
So, using the formula we get,
`S_n = 11/2 [2(2) + (11 - 1)(4)]`
`= (11/2)[4 + (10)(4)]`
`= (11/2)[4 + 40]`
`= (11/2) [44]`
= 242
Therefore, the sum of first 11 terms for the given A.P. is 242
APPEARS IN
RELATED QUESTIONS
The ratio of the sum use of n terms of two A.P.’s is (7n + 1) : (4n + 27). Find the ratio of their mth terms
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 first 13 terms of the A.P: -6, 0, 6, 12,....
How many two-digit number are divisible by 6?
How many numbers are there between 101 and 999, which are divisible by both 2 and 5?
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
Find an AP whose 4th term is 9 and the sum of its 6th and 13th terms is 40.
Find the sum of the following Aps:
9, 7, 5, 3 … to 14 terms
The sum of the first n terms in an AP is `( (3"n"^2)/2 +(5"n")/2)`. Find the nth term and the 25th term.
In an A.P. 17th term is 7 more than its 10th term. Find the common difference.
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`
Choose the correct alternative answer for the following question .
In an A.P. first two terms are –3, 4 then 21st term is ...
The first term of an A. P. is 5 and the common difference is 4. Complete the following activity and find the sum of the first 12 terms of the A. P.
a = 5, d = 4, s12 = ?
`s_n = n/2 [ square ]`
`s_12 = 12/2 [10 +square]`
`= 6 × square `
` =square`
The first and the last terms of an A.P. are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
If 18th and 11th term of an A.P. are in the ratio 3 : 2, then its 21st and 5th terms are in the ratio
A manufacturer of TV sets produces 600 units in the third year and 700 units in the 7th year. Assuming that the production increases uniformly by a fixed number every year, find:
- the production in the first year.
- the production in the 10th year.
- the total production in 7 years.
Q.6
In an A.P. (with usual notations) : given d = 5, S9 = 75, find a and a9
The ratio of the 11th term to the 18th term of an AP is 2 : 3. Find the ratio of the 5th term to the 21st term, and also the ratio of the sum of the first five terms to the sum of the first 21 terms.
The sum of all two digit numbers is ______.
