Advertisements
Advertisements
Question
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
Options
11
3
8
5
Advertisements
Solution
Here, we are given two A.P.’s with same common difference. Let us take the common difference as d.
Given,
First term of first A.P. (a) = 8
First term of second A.P. (a’) = 3
We need to find the difference between their 30th terms.
So, let us first find the 30th term of first A.P.
`a_30 = a + ( 30 -1) d`
= 8 + 29 d ...........(1)
Similarly, we find the 30th term of second A.P.
`a'_(30) = a '+ ( 30 -1) d`
= 3 + 29 d ...............(2)
Now, the difference between the 30th terms is,
`a_30 - a'_(30) = (8 + 29d) - ( 3 + 29 d) `
= 8 + 29 d - 3 - 29 d
= 8 -3
= 5
Therefore, `a_30 - a'_(30) = 5`
APPEARS IN
RELATED QUESTIONS
Find the sum of all numbers from 50 to 350 which are divisible by 6. Hence find the 15th term of that A.P.
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.
If the ratio of the sum of the first n terms of two A.Ps is (7n + 1) : (4n + 27), then find the ratio of their 9th terms.
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.
Find the sum of first 22 terms of an A.P. in which d = 22 and a = 149.
Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.
Find the sum of all natural numbers between 250 and 1000 which are divisible by 9.
If the 8th term of an A.P. is 37 and the 15th term is 15 more than the 12th term, find the A.P. Also, find the sum of first 20 terms of A.P.
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 the 9th term of an A.P. is zero then show that the 29th term is twice the 19th term?
If the common differences of an A.P. is 3, then a20 − a15 is
In an A.P., the sum of first ten terms is −150 and the sum of its next ten terms is −550. Find the A.P.
Write the sum of first n even natural numbers.
If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is
If k, 2k − 1 and 2k + 1 are three consecutive terms of an A.P., the value of k is
Obtain the sum of the first 56 terms of an A.P. whose 18th and 39th terms are 52 and 148 respectively.
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.
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
Find the sum of all even numbers from 1 to 250.
In an A.P., the sum of first n terms is `n/2 (3n + 5)`. Find the 25th term of the A.P.
