Advertisements
Advertisements
प्रश्न
Write the common difference of an A.P. whose nth term is an = 3n + 7.
Advertisements
उत्तर
In the given problem, nth term is given by, an = 3n + 7.
To find the common difference of the A.P., we need two consecutive terms of the A.P.
So, let us find the first and the second term of the given A.P.
First term (n=1) ,
a1 = 3(1) + 7
= 3 + 7
= 10
Second term ( n = 2 ),
a2 = 3 (2) + 7
= 6 + 7
= 13
Now, the common difference of the A.P. (d) = a2 - a1
= 13 - 10
= 3
Therefore, the common difference is d = 3 .
APPEARS IN
संबंधित प्रश्न
The sum of n, 2n, 3n terms of an A.P. are S1 , S2 , S3 respectively. Prove that S3 = 3(S2 – S1 )
The ratio of the sums of m and n terms of an A.P. is m2 : n2. Show that the ratio of the mth and nth terms is (2m – 1) : (2n – 1)
Show that a1, a2,..., an... form an AP where an is defined as below:
an = 9 − 5n
Also, find the sum of the first 15 terms.
In an A.P., if the first term is 22, the common difference is −4 and the sum to n terms is 64, find n.
Find the sum of all natural numbers between 250 and 1000 which are divisible by 9.
Find the value of x for which (x + 2), 2x, ()2x + 3) are three consecutive terms of an AP.
The sum of three consecutive terms of an AP is 21 and the sum of the squares of these terms is 165. Find these terms
If 18, a, (b - 3) are in AP, then find the value of (2a – b)
If the numbers (2n – 1), (3n+2) and (6n -1) are in AP, find the value of n and the numbers
Find the sum of all natural numbers between 200 and 400 which are divisible by 7.
Find the first term and common difference for the A.P.
0.6, 0.9, 1.2,1.5,...
Kargil’s temperature was recorded in a week from Monday to Saturday. All readings were in A.P. The sum of temperatures of Monday and Saturday was 5°C more than sum of temperatures of Tuesday and Saturday. If temperature of Wednesday was –30° celsius then find the temperature on the other five days.
In an A.P. the 10th term is 46 sum of the 5th and 7th term is 52. Find the A.P.
A piece of equipment cost a certain factory Rs 60,000. If it depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?
The sum of first n odd natural numbers is ______.
If 18th and 11th term of an A.P. are in the ratio 3 : 2, then its 21st and 5th terms are in the ratio
Q.11
The sum of first n terms of an A.P. whose first term is 8 and the common difference is 20 equal to the sum of first 2n terms of another A.P. whose first term is – 30 and the common difference is 8. Find n.
In an A.P., if Sn = 3n2 + 5n and ak = 164, find the value of k.
The ratio of the 11th term to the 18th term of an AP is 2 : 3. Find the ratio of the 5th term to the 21st term, and also the ratio of the sum of the first five terms to the sum of the first 21 terms.
