Advertisements
Advertisements
प्रश्न
If the first term of an A.P. is a and nth term is b, then its common difference is
पर्याय
- \[\frac{b - a}{n + 1}\]
- \[\frac{b - a}{n - 1}\]
- \[\frac{b - a}{n}\]
- \[\frac{b + a}{n - 1}\]
Advertisements
उत्तर
Here, we are given the first term of the A.P. as a and the nth term (an) as b. So, let us take the common difference of the A.P. as d.
Now, as we know,
an = a + ( n-1) d
On substituting the values given in the question, we get.
b = a + ( n - 1) d
( n - 1) d = b - a
d = \[\frac{b - a}{n - 1}\]
Therefore, d = \[\frac{b - a}{n - 1}\]
APPEARS IN
संबंधित प्रश्न
If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.
The sum of n, 2n, 3n terms of an A.P. are S1 , S2 , S3 respectively. Prove that S3 = 3(S2 – S1 )
An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term of the A.P.
Ramkali saved Rs 5 in the first week of a year and then increased her weekly saving by Rs 1.75. If in the nth week, her week, her weekly savings become Rs 20.75, find n.
Find the sum given below:
`7 + 10 1/2 + 14 + ... + 84`
If the nth term of the A.P. 9, 7, 5, ... is same as the nth term of the A.P. 15, 12, 9, ... find n.
Three numbers are in A.P. If the sum of these numbers is 27 and the product 648, find the numbers.
Find the sum of 28 terms of an A.P. whose nth term is 8n – 5.
Which term of the AP 21, 18, 15, …… is -81?
Write an A.P. whose first term is a and common difference is d in the following.
a = –19, d = –4
Find the first term and common difference for the A.P.
127, 135, 143, 151,...
The first and the last terms of an A.P. are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
If the sum of n terms of an A.P. is 2n2 + 5n, then its nth term is
Two A.P.'s have the same common difference. The first term of one of these is 8 and that of the other is 3. The difference between their 30th term is
If the sum of the first four terms of an AP is 40 and that of the first 14 terms is 280. Find the sum of its first n terms.
The sum of the first three numbers in an Arithmetic Progression is 18. If the product of the first and the third term is 5 times the common difference, find the three numbers.
Find the common difference of an A.P. whose first term is 5 and the sum of first four terms is half the sum of next four terms.
Find S10 if a = 6 and d = 3.
Find the next 4 terms of the sequence `1/6, 1/4, 1/3`. Also find Sn.
