Advertisements
Advertisements
प्रश्न
The sum of first three terms of an AP is 48. If the product of first and second terms exceeds 4 times the third term by 12. Find the AP.
Advertisements
उत्तर
Let the first three terms of the AP be (a-d) , a and (a+d) . then
(a-d) + a+(a+d) = 48
⇒ 3a = 48
⇒ a= 16
Now,
(a-d)× a = 4 (a+d) + 12 (Given)
⇒ (16-d) × 16 = 4(16 +d) +12
⇒ 256-16d = 64 +4d +12
⇒16d + 4d=256-76
⇒ 20d=180
⇒ d=9
When a = 16 and d = 9 ,
a-d = 16-9=7
a+d = 16+9=25
Hence, the first three terms of the AP are 7, 16, and 25.
APPEARS IN
संबंधित प्रश्न
If the sum of the first n terms of an A.P. is `1/2`(3n2 +7n), then find its nth term. Hence write its 20th term.
How many terms of the AP. 9, 17, 25 … must be taken to give a sum of 636?
A small terrace at a football field comprises 15 steps, each of which is 50 m long and built of solid concrete. Each step has a rise of `1/4` m and a tread of `1/2` m (See figure). Calculate the total volume of concrete required to build the terrace.
[Hint: Volume of concrete required to build the first step = `1/4 xx 1/2 xx 50 m^3`]
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 7 − 3n
Find the sum of all integers between 84 and 719, which are multiples of 5.
Find the sum of the first 13 terms of the A.P: -6, 0, 6, 12,....
The 7th term of the an AP is -4 and its 13th term is -16. Find the AP.
Kargil’s temperature was recorded in a week from Monday to Saturday. All readings were in A.P. The sum of temperatures of Monday and Saturday was 5°C more than sum of temperatures of Tuesday and Saturday. If temperature of Wednesday was –30° celsius then find the temperature on the other five days.
Find the A.P. whose fourth term is 9 and the sum of its sixth term and thirteenth term is 40.
Find out the sum of all natural numbers between 1 and 145 which are divisible by 4.
Write the value of a30 − a10 for the A.P. 4, 9, 14, 19, ....
Write the expression of the common difference of an A.P. whose first term is a and nth term is b.
If the sum of n terms of an A.P. be 3n2 + n and its common difference is 6, then its first term is ______.
If Sn denote the sum of n terms of an A.P. with first term a and common difference dsuch that \[\frac{Sx}{Skx}\] is independent of x, then
The first three terms of an A.P. respectively are 3y − 1, 3y + 5 and 5y + 1. Then, y equals
Two cars start together in the same direction from the same place. The first car goes at uniform speed of 10 km h–1. The second car goes at a speed of 8 km h–1 in the first hour and thereafter increasing the speed by 0.5 km h–1 each succeeding hour. After how many hours will the two cars meet?
In a Arithmetic Progression (A.P.) the fourth and sixth terms are 8 and 14 respectively. Find that:
(i) first term
(ii) common difference
(iii) sum of the first 20 terms.
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.
Kanika was given her pocket money on Jan 1st, 2008. She puts Rs 1 on Day 1, Rs 2 on Day 2, Rs 3 on Day 3, and continued doing so till the end of the month, from this money into her piggy bank. She also spent Rs 204 of her pocket money, and found that at the end of the month she still had Rs 100 with her. How much was her pocket money for the month?
Solve the equation:
– 4 + (–1) + 2 + 5 + ... + x = 437
