Advertisements
Advertisements
प्रश्न
If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.
उत्तर
Let the first term and the common difference of the given A.P. be a and d, respectively.
Sum of the first 7 terms, S7 = 49
We know
`S = n/2[2a + (n - 1)d]`
⇒ `7/2(2a + 6d) = 49`
⇒ `7/2 xx 2(a + 3d) = 49`
⇒ a + 3d = 7 ...(1)
Sum of the first 17 terms, S17 = 289
⇒ `17/2(2a + 16d) = 289`
⇒ `17/2 xx 2(a + 8d) = 289`
⇒ a + 8d = `289/17`
⇒ a + 8d = 17 ...(2)
Subtracting (2) from (1), we get
5d = 10
d = `5/10`
⇒ d = 2
Substituting the value of d in (1), we get
a = 1
Now,
sum of the first n terms is given by
`S_n = n/2[2a + (n - 1)d]`
= `n/2[2 xx 1 + (n - 1) xx 2]`
= `n/2 [2 + 2n - 2]`
= `n/2 [2n]`
= n2
Therefore, the sum of the first n terms of the A.P. is n2.
APPEARS IN
संबंधित प्रश्न
The first and the last terms of an AP are 8 and 65 respectively. If the sum of all its terms is 730, find its common difference.
Ramkali saved Rs 5 in the first week of a year and then increased her weekly saving by Rs 1.75. If in the nth week, her week, her weekly savings become Rs 20.75, find n.
Find the sum of the following APs.
−37, −33, −29, …, to 12 terms.
In an AP Given a12 = 37, d = 3, find a and S12.
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:
3, 9/2, 6, 15/2, ... to 25 terms
Find the sum to n term of the A.P. 5, 2, −1, −4, −7, ...,
Find the sum of the first 40 positive integers divisible by 3
Find the sum of the first 15 terms of each of the following sequences having the nth term as
bn = 5 + 2n
Find the sum of the first 22 terms of the A.P. : 8, 3, –2, ………
The 4th term of an AP is zero. Prove that its 25th term is triple its 11th term.
If 4 times the 4th term of an AP is equal to 18 times its 18th term then find its 22nd term.
The first and last terms of an AP are a and l respectively. Show that the sum of the nth term from the beginning and the nth term form the end is ( a + l ).
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
What is the sum of first n terms of the AP a, 3a, 5a, …..
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 \[\frac{\left( a + c \right) \left( b + c - 2a \right)}{2\left( b - a \right)}\].
The 19th term of an A.P. is equal to three times its sixth term. If its 9th term is 19, find the A.P.
If the seventh term of an A.P. is \[\frac{1}{9}\] and its ninth term is \[\frac{1}{7}\] , find its (63)rd term.
Which term of the sequence 114, 109, 104, ... is the first negative term?
In an AP. Sp = q, Sq = p and Sr denotes the sum of first r terms. Then, Sp+q is equal to
Sum of n terms of the series `sqrt2+sqrt8+sqrt18+sqrt32+....` is ______.
The nth term of an A.P., the sum of whose n terms is Sn, is
The sum of n terms of an A.P. is 3n2 + 5n, then 164 is its
Determine the sum of first 100 terms of given A.P. 12, 14, 16, 18, 20, ......
Activity :- Here, a = 12, d = `square`, n = 100, S100 = ?
Sn = `"n"/2 [square + ("n" - 1)"d"]`
S100 = `square/2 [24 + (100 - 1)"d"]`
= `50(24 + square)`
= `square`
= `square`
The sum of the first 2n terms of the AP: 2, 5, 8, …. is equal to sum of the first n terms of the AP: 57, 59, 61, … then n is equal to ______.
The famous mathematician associated with finding the sum of the first 100 natural numbers is ______.
Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000?
If the last term of an A.P. of 30 terms is 119 and the 8th term from the end (towards the first term) is 91, then find the common difference of the A.P. Hence, find the sum of all the terms of the A.P.
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.
k + 2, 2k + 7 and 4k + 12 are the first three terms of an A.P. The first term of this A.P. is ______.
