Progressions with equal common difference are known as
Progressions with equal common difference are known as Arithmetic Progression.
The first term of an A.P., if its Sn = n2+2n is
If the second term of an AP is 13 and its fifth term is 25, then its 7th term is
In an A.P., if am = 1/n and an = 1/m, then amn =
∴ amn = a + (mn - 1) d = 1/mn + (mn - 1)
The first term of an AP is 5, the last term is 45 and the sum is 400. The number of terms is
The value of ‘k’ for which the numbers x, 2x + k, 3x + 6 are in A.P. is
If the common difference of an A.P. is 5, then the value of a20 − a13 is
Given: a20 - a13 and d = 5
⇒ a20 - a13 = a + (20 - 1) d - [a + (13 - 1) d] = a + (20 - 1) x 5 - [a + (13 - 1) x 5]
⇒ a20 - a13 - a = a + 95 - [a + 60]
= a+95 - a - 60 = 35
Two APs have the same common difference. The difference between their 100th terms is 100, then the difference between their 1000th terms is
The common difference of the A.P whose Sn = 3n2+ 2n is
Thus, initial term of the A.P. is 5 and the common difference is 6.
The sum of (a + b), (a – b), (a – 3b), …….. to 22nd term is
First Term = a+b
Second Term = a-b
Common Difference is a-b-a-b = -2b.
Summation of 22 terms of an A.P. is
n/2 [ 2a + (n-1)d ]
22/2 [2 ( a+b) + (22-1)-2b ]
11 [ 2a+2a-b + (21)-2b ]
11 [ 2a+2b - 42b ]
11 [ 2a - 40b ]
22a - 40b.
So, the summation of given A.P. for 22 terms is 22a - 40b
The next term of the A.P. √18 , √32 and √50 is
If 9 times the 9th term of an A.P. is equal to 11 times the 11th term , then its 20th term is
The 17th term of an AP exceeds its 10th term by 7, then the common difference is
The sum of three terms of an A.P. is 72, then its middle term is
Let the middle term be a, then first term is a−d and next term is a+d
The sum of odd numbers between 0 and 50 is
Odd numbers between 0 and 50 are 1, 3, 5, 7, ………, 49 Here a = 1,d = 3−1 = 2 and
If a, b and c are in A.P., then the relation between them is given by
If a, b and c are in A.P., then
The 7th term from the end of the A.P. – 11, – 8, – 5, ……., 49 is
The number of three digit numbers divisible by 7 is
Three digits numbers divisible by 7 are 105, 112, 119,.........., 994
Here, a= 105, d = 112 - 105 = 7, an = 994
The first and last terms of an A.P. are 1 and 11. If their sum is 36, then the number of terms will be
If 1 + 4 + 7 + ……. + k = 287, then the value of ‘k’ is
If the angles of a right angled triangle are in A.P. then the angles of that triangle will be
Let the three angles of a triangle be a - d, a and a + d.
Therefore, one angle is of 60° and other is 90° (given). Let third angle be x° . then
Therefore the angles of the right angled triangle are 30°, 60°, 90°.
The 10th term of an A.P. 2, 7, 12, …….. is
If a1 = 4 and an = 4an−1+3, n >1, then the value of a4 is
The number of terms of the A.P. 5, 8, 11, 14, ……. to be taken so that the sum is 258 is
A sum of Rs.700 is to be used to award 7 prizes. If each prize is Rs.20 less than its preceding prize, then the value of the first prize is
Let the first prize be a.
The seven prizes form an AP with first term a and common difference d = −20
Now the sum of all seven prizes = Rs. 700