Advertisements
Advertisements
Question
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.
Solution
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
RELATED QUESTIONS
In an AP given a3 = 15, S10 = 125, find d and a10.
The first and last terms of an AP are 17 and 350, respectively. If the common difference is 9, how many terms are there, and what is their sum?
Find the sum of first 40 positive integers divisible by 6.
Find the sum of first 8 multiples of 3
Find the sum of the first 40 positive integers divisible by 5
Find the sum of all 3 - digit natural numbers which are divisible by 13.
Find the middle term of the AP 6, 13, 20, …., 216.
If an denotes the nth term of the AP 2, 7, 12, 17, … find the value of (a30 - a20 ).
Find the first term and common difference for the A.P.
127, 135, 143, 151,...
Find the first term and common difference for the A.P.
`1/4,3/4,5/4,7/4,...`
For an given A.P., t7 = 4, d = −4, then a = ______.
In an A.P. the first term is – 5 and the last term is 45. If the sum of all numbers in the A.P. is 120, then how many terms are there? What is the common difference?
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.
In a school, students decided to plant trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be double of the class in which they are studying. If there are 1 to 12 classes in the school and each class has two sections, find how many trees were planted by the students.
The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by \[\frac{l^2 - a^2}{k - (l + a)}\] , then k =
If the nth term of an A.P. is 2n + 1, then the sum of first n terms of the A.P. is
Q.10
The sum of the first three numbers in an Arithmetic Progression is 18. If the product of the first and the third term is 5 times the common difference, find the three numbers.
In an A.P. (with usual notations) : given d = 5, S9 = 75, find a and a9
If the nth term of an AP is (2n +1), then the sum of its first three terms is ______.
