Find first term, common difference and $5^{th}$ term of the sequence which have the following $n^{th}$ term: $3n+7$.
Given: A sequence whose $n^{th}$ term: $3n+7$.
To do: To find first term, common difference and $5^{th}$ term of the sequence.
Solution:
$n^{th}$ term, $T_n=3n+7$
$T_2=3\times2+7=13$
$T_1=3\times1+7=10$
$T_5=3\times5+7=22$
Common difference $d=T_2−T_1$
$=13−10=3$
Hence, First term $a=10$, Common difference $d=3$ and Fifth term $T_5=22$
Related Articles
- Find the \( 20^{\text {th }} \) term of the AP whose \( 7^{\text {th }} \) term is 24 less than the \( 11^{\text {th }} \) term, first term being 12.
- If $(m + 1)$th term of an A.P. is twice the $(n + 1)$th term, prove that $(3m + 1)$th term is twice the $(m + n + 1)$th term.
- The pattern of a term is 2, 5, 8, 11, 14,... and its general term is $3n-1$. Find the $50^{th} $ term.
- If the $2^{nd}$ term of an A.P. is $13$ and the $5^{th}$ term is $25$, what is its $7^{th}$ term?
- If $m$ times the $m^{th}$ term of an AP is equal to $n$ times its $n^{th}$ term. find the $( m+n)^{th}$ term of the AP.
- 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.
- If the sum of the first $n$ terms of an AP is $\frac{1}{2}(3n^2+7n)$ then find its $n^{th}$ term. Hence, find its $20^{th}$ term.
- If an A.P. consists of $n$ terms with first term $a$ and $n$th term $l$ show that the sum of the $m$th term from the beginning and the $m$th term from the end is $(a + l)$
- 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
- If the $n^{th}$ term of an AP is $\frac{3+n}{4}$, then find its $8^{th}$ term.
- 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.
- If eight times the $8^{th}$ term of an arithmetic progression is equal to seventeen times the $7^{th}$ term of the progression, find the $15^{th}$ term of the progression.
- 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.
- The $9^{th}$ term of an AP is $499$ and its $499^{th}$ term is $9$. Which of its term is equal to zero.
- 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.
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