Advertisements
Advertisements
प्रश्न
The sum of the first three terms of an Arithmetic Progression (A.P.) is 42 and the product of the first and third term is 52. Find the first term and the common difference.
Advertisements
उत्तर
Let the three times terms of an A.P. be (a - d ),a, (a + d)
sum = 42 = (a - d) + a + (a + d)
42 = 3a
⇒ ` a = 42/3`
⇒ a = 14
Also , (a - d ) (a + d) = 52
⇒ ` a^2 - d^2 = 52 `
`d^2 = a^2 - 52`
` = 196 - 52 `
`d^2 = 144`
⇒ `d = +- 12`
∴ First term ` = {(a - d,=,14,+,12,=,26),(a + d,=,14,-,12,=,2):}`
∴ A.P. is 2, 14, 26 or 26,14,2
APPEARS IN
संबंधित प्रश्न
Find the sum of the following APs.
0.6, 1.7, 2.8, …….., to 100 terms.
How many two-digits numbers are divisible by 3?
How many three-digit numbers are divisible by 9?
Find the value of x for which (x + 2), 2x, ()2x + 3) are three consecutive terms of an AP.
Find the first term and common difference for the A.P.
0.6, 0.9, 1.2,1.5,...
The sum of the first n terms of an A.P. is 4n2 + 2n. Find the nth term of this A.P.
The sum of the first 2n terms of the AP: 2, 5, 8, …. is equal to sum of the first n terms of the AP: 57, 59, 61, … then n is equal to ______.
Find the sum of first 'n' even natural numbers.
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?
If the last term of an A.P. of 30 terms is 119 and the 8th term from the end (towards the first term) is 91, then find the common difference of the A.P. Hence, find the sum of all the terms of the A.P.
