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`
RELATED QUESTIONS
How many terms of the series 54, 51, 48, …. be taken so that their sum is 513 ? Explain the double answer
Determine the A.P. whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
Find the sum of the following APs:
–37, –33, –29, ... to 12 terms.
Find the sum of the following arithmetic progressions:
–26, –24, –22,... to 36 terms
Find the sum of all odd numbers between 100 and 200.
The 24th term of an AP is twice its 10th term. Show that its 72nd term is 4 times its 15th term.
Choose the correct alternative answer for the following question.
For an given A.P. a = 3.5, d = 0, n = 101, then tn = ....
There are 25 rows of seats in an auditorium. The first row is of 20 seats, the second of 22 seats, the third of 24 seats, and so on. How many chairs are there in the 21st row ?
Fill up the boxes and find out the number of terms in the A.P.
1,3,5,....,149 .
Here a = 1 , d =b`[ ], t_n = 149`
tn = a + (n-1) d
∴ 149 =`[ ] ∴149 = 2n - [ ]`
∴ n =`[ ]`
Find the sum of all 2-digit natural numbers divisible by 4.
Find the sum:
\[18 + 15\frac{1}{2} + 13 + ... + \left( - 49\frac{1}{2} \right)\]
Find the sum of n terms of the series \[\left( 4 - \frac{1}{n} \right) + \left( 4 - \frac{2}{n} \right) + \left( 4 - \frac{3}{n} \right) + ....\]
Q.4
Q.16
Q.20
Obtain the sum of the first 56 terms of an A.P. whose 18th and 39th terms are 52 and 148 respectively.
For an A.P., if t1 = 1 and tn = 149, then find Sn.
Activitry :- Here t1= 1, tn = 149, Sn = ?
Sn = `n/2 (square + square)`
= `n/2 xx square`
= `square` n, where n = 75
If the last term of an A.P. of 30 terms is 119 and the 8th term from the end (towards the first term) is 91, then find the common difference of the A.P. Hence, find the sum of all the terms of the A.P.
Find the sum of first 16 terms of the A.P. whose nth term is given by an = 5n – 3.
Which expression gives the sum of the first n natural numbers \[1 + 2 + \cdots + n\]?
