If the common difference of an A.P. is 3, then$\ a_{20} -a_{15}$ is
$( A)\ 5$
$( B)\ 3$
$( C)\ 15$
$( D)\ 20$
Given: Common difference of an A.P., $d=3$
To do: To find out the value of $a_{20} -a_{15}=?$
Solution: let us say firrst term of A.P. is$a$.
As we know nth term of an A.P. with first term a and common difference d
$n^{th}$ term of the given A.P.,$a_{n} =a\ +( n-1) d$
Then $a_{20} =a+( n-1) d$
$=a+( 20-1) \times 3$
$=a+57$
Similiarly $a_{15} =a+( 15-1) \times 3$
$=a+42$
$\therefore a_{20} -a_{15} =( a+57) -( a+42)$
$=a+57-a-42$
$=15$
$\therefore$Option $( C)$ is correct.
Related Articles
- If the common difference of an AP is $5$, then what is $a_{18} – a_{13}$?
- Choose the correct answer from the given four options:If the common difference of an AP is 5 , then what is \( a_{18}-a_{13} \) ?(A) 5(B) 20(C) 25(D) 30
- If \( a_{n}=3-4 n \), show that \( a_{1}, a_{2}, a_{3}, \ldots \) form an AP. Also find \( S_{20} \).
- For the A.P.: $-3, -7, -11,…,$ can we find $a_{30} – a_{20}$ without actually finding $a_{30}$ and $a_{20}$? Give reasons for your answer.
- For the \( A P-3,-7,-11, \ldots \), without finding \( a_{30} \) and \( a_{20} \) inpidually, find \( a_{30}-a_{20} \).
- Find $a_{30} - a_{20}$ for the A.P.$a, a + d, a + 2d, a + 3d, …$
- What is the common difference of an A.P. in which $a_{21} -a_{7} = 84?$
- Find $a_{30} - a_{20}$ for the A.P.$-9, -14, -19, -24, …$
- For the AP: \( -3,-7,-11, \ldots \), can we find directly \( a_{30}-a_{20} \) without actually finding \( a_{30} \) and \( a_{20} \) ? Give reasons for your answer.
- Justify whether it is true to say that \( -1,-\frac{3}{2},-2, \frac{5}{2}, \ldots \) forms an AP as \( a_{2}-a_{1}=a_{3}-a_{2} . \)
- Choose the correct answer from the given four options:In an \( \mathrm{AP} \), if \( d=-4, n=7, a_{n}=4 \), then \( a \) is(A) 6(B) 7(C) 20(D) 28
- In an AP, if the common difference $(d) = –4$, and the seventh term $( a_{7})$ is 4, then find the first term.
- Find the indicated terms in each of the following sequences whose nth terms are: \( a_{n}=5 n-4 ; a_{12} \) and \( a_{15} \)
- Choose the correct answer from the given four options:What is the common difference of an AP in which \( a_{18}-a_{14}=32 \) ?(A) 8(B) \( -8 \)(C) \( -4 \)(D) 4
- Find the value of $\frac{3}{20} + \frac{8}{15}$.
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies