Advertisements
Advertisements
प्रश्न
Find the sum of the following arithmetic progressions: 50, 46, 42, ... to 10 terms
Advertisements
उत्तर
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
50, 46, 42, ... to 10 terms
Common difference of the A.P. (d)
`= a_2 - a_1`
= 46 - 50
= -4
Number of terms (n) = 10
First term for the given A.P. (a) = 50
So using the formula we get
`S_10 = 10/2 [2(50) + (10 - 1)(-4)]`
= (5)[100 + (9)(-4)]
= (5)[100 - 36]
= (5)[64]
= 320
Therefore the sum of first 10 terms for the given A.P is 320
APPEARS IN
संबंधित प्रश्न
Ramkali required Rs 2,500 after 12 weeks to send her daughter to school. She saved Rs 100 in the first week and increased her weekly saving by Rs 20 every week. Find whether she will be able to send her daughter to school after 12 weeks.
What value is generated in the above situation?
If the term of m terms of an A.P. is the same as the sum of its n terms, show that the sum of its (m + n) terms is zero
In an AP Given a12 = 37, d = 3, find a and S12.
In an AP given a = 3, n = 8, Sn = 192, find d.
The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 7 − 3n
The 24th term of an AP is twice its 10th term. Show that its 72nd term is 4 times its 15th term.
Find the sum of the following Aps:
i) 2, 7, 12, 17, ……. to 19 terms .
Write an A.P. whose first term is a and common difference is d in the following.
a = –1.25, d = 3
First term and the common differences of an A.P. are 6 and 3 respectively; find S27.
Solution: First term = a = 6, common difference = d = 3, S27 = ?
Sn = `"n"/2 [square + ("n" - 1)"d"]` - Formula
Sn = `27/2 [12 + (27 - 1)square]`
= `27/2 xx square`
= 27 × 45
S27 = `square`
Simplify `sqrt(50)`
The sum of first n terms of an A.P. is 3n2 + 4n. Find the 25th term of this A.P.
Write the nth term of the \[A . P . \frac{1}{m}, \frac{1 + m}{m}, \frac{1 + 2m}{m}, . . . .\]
The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is
If the sum of first n terms of an AP is An + Bn² where A and B are constants. The common difference of AP will be ______.
Find the sum:
`(a - b)/(a + b) + (3a - 2b)/(a + b) + (5a - 3b)/(a + b) +` ... to 11 terms
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.
Rohan repays his total loan of ₹ 1,18,000 by paying every month starting with the first installment of ₹ 1,000. If he increases the installment by ₹ 100 every month, what amount will be paid by him in the 30th installment? What amount of loan has he paid after 30th installment?
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.
