Advertisements
Advertisements
प्रश्न
Determine the A.P. whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
Advertisements
उत्तर
We have given a3 = 16
a + (3 − 1)d = 16
a + 2d = 16(1)
a7 − a5 = 12
[a + (7 − 1)d] − [a + (5 − 1)d] = 12
(a + 6d) − (a + 4d) = 12
2d = 12
d = 6
From equation (1), we obtain
a + 2(6) = 16
a + 12 = 16
a = 4
Therefore, A.P. will be 4, 10, 16, 22, ...
APPEARS IN
संबंधित प्रश्न
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line.
A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
[Hint: to pick up the first potato and the second potato, the total distance (in metres) run by a competitor is 2 × 5 + 2 × (5 + 3)]
The nth term of an A.P. is given by (–4n + 15). Find the sum of first 20 terms of this A.P.
Sum of 1 to n natural numbers is 36, then find the value of n.
In a school, students decided to plant trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be double of the class in which they are studying. If there are 1 to 12 classes in the school and each class has two sections, find how many trees were planted by the students.
If `4/5`, a, 2 are three consecutive terms of an A.P., then find the value of a.
If the sum of first p term of an A.P. is ap2 + bp, find its common difference.
Write the nth term of the \[A.P. \frac{1}{m}, \frac{1 + m}{m}, \frac{1 + 2m}{m}, . . . .\]
The common difference of the A.P. is \[\frac{1}{2q}, \frac{1 - 2q}{2q}, \frac{1 - 4q}{2q}, . . .\] is
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?
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]
