The sum of the A.P. with $21$ terms is $210$, then find the $11^{th}$ term.
Given: The sum of the A.P. with $21$ terms is $210$.
To do: To find the $11^{th}$ term.
Solution:
Sum of $n$ terms in A.P.$=\frac{n}{2}( 2a+( n-1)d)$
$\Rightarrow 210=\frac{21}{2}(2a+20d)$
$\Rightarrow 210\times \frac{2}{21}=(2a+20d)$
$\Rightarrow \frac{420}{21}=(2a+20d)$
$\Rightarrow 20=2a+20d$
dividing both sides by $2$ we get
$10=a+10d$
We want to find the value of $11^{th}$ term
$=a+(11-1)d$
$=a+10d$
$=10$
Thus, $11^{th}$ term of the A.P. is $10$.
Related Articles
- The $14^{th}$ term of an A.P. is twice its $8^{th}$ term. If its $6^{th}$ term is $-8$, then find the sum of its first $20$ terms.
- If the 10th term of an A.P. is 21 and the sum of its first ten terms is 120, find its $n$th term.
- If $7$ times of the $7^{th}$ term of an A.P. is equal to $11$ times its $11^{th}$ term, then find its $18^{th}$ term.
- In an A.P. the sum of $n$ terms is $5n^2−5n$. Find the $10^{th}$ term of the A.P.
- Find the number of terms of the A.P. $-12, -9, -6,........21$. If 1 is added to each term of this A.P. then find the sum of all terms of the A.P. thus obtained.
- The $4^{th}$ term of an A.P. is zero. Prove that the $25^{th}$ term of the A.P. is three times its $11^{th}$ term.
- The sum of first n terms of an A.P. is $3n^{2} +4n$. Find the $25^{th}$ term of this A.P.
- If the $6^{th}$ term of an A.S is 64, find the sum of the first 11 terms.
- If the $10^{th}$ term of an A.P is $\frac{1}{20}$ and its $20^{th}$ term is $\frac{1}{10}$, then find the sum of its first $200$ terms.
- Find the $5^{th}$ term of an A.P. of $n$ terms whose sum is $n^2−2n$.
- The $m^{th}$ term of an arithmetic progression is $x$ and the $n^{th}$ term is $y$. Then find the sum of the first $( m+n)$ terms.
- The ratio of the \( 11^{\text {th }} \) term to the \( 18^{\text {th }} \) term of an AP is \( 2: 3 \). Find the ratio of the \( 5^{\text {th }} \) term to the 21 term
- Find the largest term common to the sequences $1,\ 11,\ 21,\ 31,\ ...$ to $100^{th}$ terms and $31,\ 36,\ 41,\ 46,\ ...$ to $100^{th}$ terms.
- In an AP of 50 terms, the sum of first 10 terms is 210 and the sum of its last 15 terms is 2565. Find the A.P.
- The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceeds the second term by 6, find three terms.
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