Advertisements
Advertisements
Question
Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.
−225, −425, −625, −825, ...
Solution
In the given problem, we are given various sequences.
We need to find out that the given sequences are an A.P or not and then find its common difference (d)
−225, −425, −625, −825, ...
Here
First term (a) = −225
`a_1 = -425`
`a_2 = -625`
Now, for the given to sequence to be an A.P,
Common difference (d) = `a_1 - a = a_2 - a_1`
Here
`a_1 - a = -425 - (-225)`
= -200
Also
`a_2 - a_1 = -625 - (-425)`
= -200
Since `a_1 - a = a_2 - a_1`
Hence, the given sequence is an A.P and its common difference is d = -200
APPEARS IN
RELATED QUESTIONS
If the nth term of a progression be a linear expression in n, then prove that this progression is an AP
Which term of the sequence 4, 9 , 14, 19, …… is 124 ?
Following are APs or not? If they form an A.P. find the common difference d and write three more terms:
0.2, 0.22, 0.222, 0.2222 ….
Following are APs or not? If they form an A.P. find the common difference d and write three more terms:
`sqrt2, sqrt8, sqrt18, sqrt32 ...`
What is the common difference of an A.P. in which a21 – a7 = 84?
Find the nth term of the A.P. 13, 8, 3, −2, ...
Write the expression an- ak for the A.P. a, a + d, a + 2d, ... Hence, find the common difference of the A.P. for which
20th term is 10 more than the 18th term.
Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.
The product of four consecutive positive integers is 840. Find the numbers.
Two APs have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any two corresponding terms. Why?
