Advertisements
Advertisements
Question
Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.
1.0, 1.7, 2.4, 3.1, ...
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)
1.0, 1.7, 2.4, 3.1, ...
Here,
First term (a) = 1.0
`a_1 = 1.7`
`a_2 = 2.4`
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 = 1.7 - 1.0`
= 0.7
Also
`a_2 - a_1 = 2.4 - 1.7`
= 0.7
Since `a_1 - a = a_2 - a_1`
Hence, the given sequence is an A.P and its common difference is d = 0.7
APPEARS IN
RELATED QUESTIONS
Write the first five terms of the sequence defined by `a_n = (–1)^(n-1) . 2^n`
Write first four terms of the A.P. when the first term a and the common difference d are given as follows:
a = -1.25, d = -0.25
Following are APs or not? If they form an A.P. find the common difference d and write three more terms:
`2, 5/2, 3, 7/2 ....`
The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last term to the product of two middle terms is 7: 15. Find the numbers.
Find the value of x for which (8x + 4), (6x − 2) and (2x + 7) are in A.P.
Write the two terms of the A.P. 2,5,8,11,...
In an A.P. t10 = 57 and t15 = 87, then find t21
Justify whether it is true to say that `-1, - 3/2, -2, 5/2,...` forms an AP as a2 – a1 = a3 – a2.
Which term in the A.P. 60, 56, 52, 48, 44, 40, ...... is the first negative term?
The next term of the A.P. : `sqrt(6), sqrt(24), sqrt(54)` is ______.
