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
How many terms of the A.P. 18, 16, 14, .... be taken so that their sum is zero?
A small terrace at a football field comprises 15 steps, each of which is 50 m long and built of solid concrete. Each step has a rise of `1/4` m and a tread of `1/2` m (See figure). Calculate the total volume of concrete required to build the terrace.
[Hint: Volume of concrete required to build the first step = `1/4 xx 1/2 xx 50 m^3`]
If the pth term of an A. P. is `1/q` and qth term is `1/p`, prove that the sum of first pq terms of the A. P. is `((pq+1)/2)`.
Find the sum of the following arithmetic progressions:
`(x - y)/(x + y),(3x - 2y)/(x + y), (5x - 3y)/(x + y)`, .....to n terms
The 4th term of an AP is zero. Prove that its 25th term is triple its 11th term.
How many two-digits numbers are divisible by 3?
The angles of quadrilateral are in whose AP common difference is 10° . Find the angles.
Rs 1000 is invested at 10 percent simple interest. Check at the end of every year if the total interest amount is in A.P. If this is an A.P. then find interest amount after 20 years. For this complete the following activity.
Find the sum (−5) + (−8)+ (−11) + ... + (−230) .
In an A.P. the first term is 8, nth term is 33 and the sum to first n terms is 123. Find n and d, the common differences.
The sum of first n terms of an A.P. is 3n2 + 4n. Find the 25th term of this A.P.
If the sum of n terms of an A.P. is Sn = 3n2 + 5n. Write its common difference.
Two cars start together in the same direction from the same place. The first car goes at uniform speed of 10 km h–1. The second car goes at a speed of 8 km h–1 in the first hour and thereafter increasing the speed by 0.5 km h–1 each succeeding hour. After how many hours will the two cars meet?
Q.3
Shubhankar invested in a national savings certificate scheme. In the first year he invested ₹ 500, in the second year ₹ 700, in the third year ₹ 900 and so on. Find the total amount that he invested in 12 years
A merchant borrows ₹ 1000 and agrees to repay its interest ₹ 140 with principal in 12 monthly instalments. Each instalment being less than the preceding one by ₹ 10. Find the amount of the first instalment
The famous mathematician associated with finding the sum of the first 100 natural numbers is ______.
Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000?
Find the middle term of the AP. 95, 86, 77, ........, – 247.
Three numbers in A.P. have the sum of 30. What is its middle term?
