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प्रश्न
Show that each of the progressions given below is an AP. Find the first term, common difference and next term of each .
(iii)-1 `, (-5)/6 , (-2)/3 , (-1)/2 ............`
उत्तर
The given progression -1 `, (-5)/6 , (-2)/3 , (-1)/2 ............`
Clearly, ` (-5)/6 - (-1) = (-2)/3 - ((-5)/6) = (-1)/2- ((-2)/3 ) = 1/6 `(Constant)
Thus, each term differs from its preceding term by`1/6` So, the given progression is an
AP.
First term = –1
Common difference =`1/6`
Next tern of the AP = `(-1)/2 + 1/6 = (-2)/6 = (-1)/3`
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संबंधित प्रश्न
Fill in the blank in the following table, given that a is the first term, d the common difference, and an nth term of the AP:
| a | d | n | an |
| 7 | 3 | 8 | ______ |
The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the A.P.
An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find the 32nd term.
The sum of 4th and 8th terms of an A.P. is 24 and the sum of 6th and 10th terms is 44. Find the A.P.
Find the nth term of the following Aps:
16, 9, 2, -5, …..
If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term?
If the common difference of an AP is 5, then what is a18 – a13?
Write the first three terms of the APs when a and d are as given below:
a = –5, d = –3
Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20.
What is the common difference of an AP in which a18 – a14 = 32?
