Advertisements
Advertisements
प्रश्न
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 7 − 3n
Advertisements
उत्तर
Here, we are given an A.P. whose nth term is given by the following expression, `a_n = 7 - 3n`. We need to find the sum of first 25 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 nth term of A.P.
a = 7 - 3(1)
= 7 - 3
= 4
Now, the last term (l) or the nth term is given
`l = a_n = 7 - 3n`
So, on substituting the values in the formula for the sum of n terms of an A.P., we get,
`S_25= (258/2)[(4) + 7 - 3 (25)]`
`= (25/2) [11 - 75]`
`= (25/2) (-64)`
= (25)(-32)
= -800
Therefore, the sum of the 25 terms of the given A.P. is `S_n = -800`
APPEARS IN
संबंधित प्रश्न
Find the sum of first 30 terms of an A.P. whose second term is 2 and seventh term is 22
Find the sum of the following arithmetic progressions
`(x - y)^2,(x^2 + y^2), (x + y)^2,.... to n term`
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 2 + 4 + 6 ... + 200
Find the sum of two middle most terms of the AP `-4/3, -1 (-2)/3,..., 4 1/3.`
The 19th term of an AP is equal to 3 times its 6th term. If its 9th term is 19, find the AP.
How many three-digit natural numbers are divisible by 9?
Two A.P.’s are given 9, 7, 5, ... and 24, 21, 18, ... If nth term of both the progressions are equal then find the value of n and nth term.
If the sum of first p terms of an A.P. is equal to the sum of first q terms then show that the sum of its first (p + q) terms is zero. (p ≠ q)
If the sum of first n terms of an A.P. is \[\frac{1}{2}\] (3n2 + 7n), then find its nth term. Hence write its 20th term.
If the sums of n terms of two arithmetic progressions are in the ratio \[\frac{3n + 5}{5n - 7}\] , then their nth terms are in the ratio
If the sum of the first four terms of an AP is 40 and that of the first 14 terms is 280. Find the sum of its first n terms.
How many terms of the A.P. 24, 21, 18, … must be taken so that the sum is 78? Explain the double answer.
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:
1 + (–2) + (–5) + (–8) + ... + (–236)
In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021-22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year. |
Based on the above information answer the following questions.
- Find the production in the 1st year
- Find the production in the 12th year.
- Find the total production in first 10 years.
[OR]
In how many years will the total production reach 31200 cars?
Find the sum of all 11 terms of an A.P. whose 6th term is 30.
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.
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.
An Arithmetic Progression (A.P.) has 3 as its first term. The sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference of the A.P.
