Advertisements
Advertisements
Question
Write the value of a30 − a10 for the A.P. 4, 9, 14, 19, ....
Advertisements
Solution
In this problem, we are given an A.P. and we need to find a30 - a10.
A.P. is 4,9,14,19 .....
Here,
First term (a) = 4
Common difference of the A.P. (d) = 9 -4
= 5
Now, as we know,
an = a + (n- 1) d
Here, we find a30 and a20.
So, for 30th term,
a30 = a + (30 - 1 ) d
= 4 + (29)(5)
= 4 + 145
= 149
Also, for 10th term,
a20 = a +(10-1) d
= 4 + (9 ) (5)
= 4 + 45
= 49
So,
a30 - a10 = 149 - 49
= 100
Therefore, for the given A.P a30 - a10 = 100 .
APPEARS IN
RELATED QUESTIONS
How many terms of the A.P. 18, 16, 14, .... be taken so that their sum is zero?
The sum of n terms of three arithmetical progression are S1 , S2 and S3 . The first term of each is unity and the common differences are 1, 2 and 3 respectively. Prove that S1 + S3 = 2S2
Find the 20th term from the last term of the A.P. 3, 8, 13, …, 253.
If the 10th term of an AP is 52 and 17th term is 20 more than its 13th term, find the AP
Find the 8th term from the end of the AP 7, 10, 13, ……, 184.
Find four numbers in AP whose sum is 8 and the sum of whose squares is 216.
The first three terms of an AP are respectively (3y – 1), (3y + 5) and (5y + 1), find the value of y .
Find four consecutive terms in an A.P. whose sum is 12 and sum of 3rd and 4th term is 14.
(Assume the four consecutive terms in A.P. are a – d, a, a + d, a +2d)
If Sn denote the sum of n terms of an A.P. with first term a and common difference dsuch that \[\frac{Sx}{Skx}\] is independent of x, then
The common difference of the A.P. \[\frac{1}{2b}, \frac{1 - 6b}{2b}, \frac{1 - 12b}{2b}, . . .\] is
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.17
Find the sum of first 10 terms of the A.P.
4 + 6 + 8 + .............
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 first 15 terms of an A.P. is 750 and its first term is 15. Find its 20th term.
In an A.P., the sum of its first n terms is 6n – n². Find is 25th term.
Find the sum of first seven numbers which are multiples of 2 as well as of 9.
The 5th term and the 9th term of an Arithmetic Progression are 4 and – 12 respectively.
Find:
- the first term
- common difference
- sum of 16 terms of the AP.
Three numbers in A.P. have the sum of 30. What is its middle term?
