Advertisements
Advertisements
Question
Find the sum of the following arithmetic progressions:
a + b, a − b, a − 3b, ... to 22 terms
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
a + b, a − b, a − 3b, ... to 22 terms]
Common difference of the A.P. (d) = `a_2 - a_1`
= (a - b) -(a + b)
= a - b - a - b
= -2b
Number of terms (n) = 22
The first term for the given A.P. (a) = a + b
So, using the formula we get,
`S_22 = 22/2 [2(a + b) + (22- 1)(-2b)]`
`= (11)[2a + 2b + (21)(-2b)]`
`= (11)[2a + 2b - 42b]`
= 22a - 440b
Therefore the sum of first 22 terms for the give A.P is 22a - 440b
APPEARS IN
RELATED QUESTIONS
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.
The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
Divide 32 into four parts which are in A.P. such that the product of extremes is to the product of means is 7 : 15.
If the 12th term of an A.P. is −13 and the sum of the first four terms is 24, what is the sum of first 10 terms?
Find the sum of all natural numbers between 1 and 100, which are divisible by 3.
Find the sum of all odd numbers between 100 and 200.
Find the sum of the first 11 terms of the A.P : 2, 6, 10, 14, ...
Find the sum of the first 51 terms of the A.P: whose second term is 2 and the fourth term is 8.
Find the sum of all natural numbers between 250 and 1000 which are divisible by 9.
How many numbers are there between 101 and 999, which are divisible by both 2 and 5?
Write the next term for the AP` sqrt( 8), sqrt(18), sqrt(32),.........`
Find the sum of all natural numbers between 200 and 400 which are divisible by 7.
For an given A.P., t7 = 4, d = −4, then a = ______.
The common difference of an A.P., the sum of whose n terms is Sn, is
The sum of first n odd natural numbers is ______.
Q.2
Q.16
If the sum of the first m terms of an AP is n and the sum of its n terms is m, then the sum of its (m + n) terms will be ______.
Find the sum:
`(a - b)/(a + b) + (3a - 2b)/(a + b) + (5a - 3b)/(a + b) +` ... to 11 terms
Assertion (A): a, b, c are in A.P. if and only if 2b = a + c.
Reason (R): The sum of first n odd natural numbers is n2.
