Advertisements
Advertisements
प्रश्न
If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.
Advertisements
उत्तर
Let a and d be the first term and common difference, respectively of an AP.
∵ Sum of n terms of an AP,
Sn = `n/2 [2a + (n - 1)d]` ...(i)
Now, S6 = 36 ...[Given]
⇒ `6/2[2a + (6 - 1)d]` = 36
⇒ 2a + 5d = 12 ...(ii)
And S16 = 256
⇒ `16/2[2a + (16 - 1)d]` = 256
⇒ 2a + 15d = 32 ...(iii)
On subtracting equation (ii) from equation (iii), we get
10d = 20
⇒ d = 2
From equation (ii),
2a + 5(2) = 12
⇒ 2a = 12 − 10 = 2
⇒ a = 1
∴ S10 = `10/2 [2a + (10 - 1)d]`
= 5[2(1) + 9(2)]
= 5(2 + 18)
= 5 × 20
= 100
Hence, the required sum of first 10 terms is 100.
APPEARS IN
संबंधित प्रश्न
Check whether -150 is a term of the A.P. 11, 8, 5, 2, ....
In an AP, given a = 7, a13 = 35, find d and S13.
In an AP Given a12 = 37, d = 3, find a and S12.
Find the sum of first 40 positive integers divisible by 6.
A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.
A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A of radii 0.5, 1.0 cm, 1.5 cm, 2.0 cm, .... as shown in figure. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take `pi = 22/7`)
[Hint: Length of successive semicircles is l1, l2, l3, l4, ... with centres at A, B, A, B, ... respectively.]
200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how many rows are the 200 logs placed, and how many logs are in the top row?
A ladder has rungs 25 cm apart. (See figure). The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and bottom rungs are 2 `1/2` m apart, what is the length of the wood required for the rungs?
[Hint: number of rungs = `250/25+ 1`]
If (m + 1)th term of an A.P is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term.
How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40?
Find the sum of first n odd natural numbers
Find the sum of the first 11 terms of the A.P : 2, 6, 10, 14, ...
Find the sum of all 3 - digit natural numbers which are divisible by 13.
Divide 24 in three parts such that they are in AP and their product is 440.
If the numbers a, 9, b, 25 from an AP, find a and b.
Write the next term of the AP `sqrt(2) , sqrt(8) , sqrt(18),.........`
Find the sum of all multiples of 9 lying between 300 and 700.
If the 9th term of an A.P. is zero then show that the 29th term is twice the 19th term?
Find where 0 (zero) is a term of the A.P. 40, 37, 34, 31, ..... .
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.
A piece of equipment cost a certain factory Rs 60,000. If it depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?
If Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to
The common difference of the A.P. is \[\frac{1}{2q}, \frac{1 - 2q}{2q}, \frac{1 - 4q}{2q}, . . .\] is
Q.3
Q.11
The middle most term(s) of the AP: -11, -7, -3,.... 49 is ______.
The sum of all two digit odd numbers is ______.
The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.
Find the middle term of the AP. 95, 86, 77, ........, – 247.
If the first term of an A.P. is p, second term is q and last term is r, then show that sum of all terms is `(q + r - 2p) xx ((p + r))/(2(q - p))`.
