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प्रश्न
Which of the following sequences are arithmetic progressions? For those which are arithmetic progressions, find out the common difference.
−225, −425, −625, −825, ...
उत्तर
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
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संबंधित प्रश्न
State whether the following sequence is an AP or not: 1, 3, 6, 10………
For what value of k will k + 9, 2k – 1 and 2k + 7 are the consecutive terms of an A.P?
Determine the general term of an A.P. whose 7th term is –1 and 16th term 17
Write first four terms of the A.P. when the first term a and the common differenced are given as follows:
a = 10, d = 10
If the 10th term of an A.P. is 52 and the 17th term is 20 more than the 13th term, find the A.P.
Find the 10th term of the AP 1,4, 7, 10….
In an A.P., if the 12th term is −13 and the sum of its first four terms is 24, find the sum of its first ten terms ?
Justify whether it is true to say that `-1, - 3/2, -2, 5/2,...` forms an AP as a2 – a1 = a3 – a2.
For an A.P., if a = 7 and d = 2.5 then t12 = ?
Statement A (Assertion): `-5, (-5)/2, 0, 5/2`, .... is in Arithmetic Progression.
Statement R (Reason): The terms of an Arithmetic Progression cannot have both positive and negative rational numbers.
