Advertisements
Advertisements
प्रश्न
Find the sum of first 20 terms of the sequence whose nth term is `a_n = An + B`
Advertisements
उत्तर
Here, we are given an A.P. whose nth term is given by the following expression `a_n = An +B`.
We need to find the sum of first 20 terms.
So, here we can find the sum of the n terms of the given A.P., using the formula,
`S_n = (n/2) (a + l)`
Where a = the first term
l = the last term
So, for the given A.P,
The first term (a) will be calculated using n = 1 in the given equation for the nth term of A.P.
a = A(1) + B
= A + B
Now, the last term (l) or the nth term is given
`I = a_n = An + B`
So, on substituting the values in the formula for the sum of n terms of an A.P., we get,
`S_20 = (20/2)[(A + B) + A(20) + B]`
= 10[21A + 2B]
= 210A + 20B
Therefore the sum of the first 20 terms of the given A.P is `S_20 = 210A + 20B`
APPEARS IN
संबंधित प्रश्न
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.
If the mth term of an A.P. is 1/n and the nth term is 1/m, show that the sum of mn terms is (mn + 1)
If the 3rd and the 9th terms of an AP are 4 and –8 respectively, which term of this AP is zero?
Find the sum of the first 15 terms of each of the following sequences having the nth term as
`a_n = 3 + 4n`
Which term of AP 72,68,64,60,… is 0?
The sequence −10, −6, −2, 2, ... is ______.
Sum of 1 to n natural numbers is 36, then find the value of n.
The first and the last terms of an A.P. are 8 and 350 respectively. If its common difference is 9, how many terms are there and what is their sum?
In an A.P. the first term is 8, nth term is 33 and the sum to first n terms is 123. Find n and d, the common differences.
If the first term of an A.P. is 2 and common difference is 4, then the sum of its 40 terms is
The given terms are 2k + 1, 3k + 3 and 5k − 1. find AP.
Q.3
Find the sum of the first 10 multiples of 6.
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.
What is the sum of an odd numbers between 1 to 50?
Find the sum of the integers between 100 and 200 that are
- divisible by 9
- not divisible by 9
[Hint (ii) : These numbers will be : Total numbers – Total numbers divisible by 9]
The sum of the 4th and 8th term of an A.P. is 24 and the sum of the 6th and 10th term of the A.P. is 44. Find the A.P. Also, find the sum of first 25 terms of the A.P.
The nth term of an Arithmetic Progression (A.P.) is given by the relation Tn = 6(7 – n)..
Find:
- its first term and common difference
- sum of its first 25 terms
The sum of n terms of an A.P. is 3n2. The second term of this A.P. is ______.
