Which term of the progression $20,\ 19\frac{1}{4} ,\ 18\frac{1}{2} ,\ 17\frac{3}{4} ,\ .............$ is the first negative term ?
Given: The progression $20,\ 19\frac{1}{4} ,\ 18\frac{1}{2} ,\ 17\frac{3}{4} ,\ .............$
To do: To find the the first negative term of the given progression.
Solution:
Given progression $20,\ 19\frac{1}{4} ,\ 18\frac{1}{2} ,\ 17\frac{3}{4} ,\ .............$
This is an Arithmetic progression because Common difference $( d) \ =19\frac{1}{4} -20=18\frac{1}{2} -9\frac{1}{4}$
$d=\frac{-3}{4}$
Any term $a_{n} =20\ ( n-1) d=20\ ( n-1)\frac{-3}{4}$
Any term $a_{n} < 0$ when $83\ < 3n\ $
This is valid for $n=28$ and $28^{th}$ term will be the first negative term.
Related Articles
- Which is greater in each of the following:$(i)$. $\frac{2}{3},\ \frac{5}{2}$$(ii)$. $-\frac{5}{6},\ -\frac{4}{3}$$(iii)$. $-\frac{3}{4},\ \frac{2}{-3}$$(iv)$. $-\frac{1}{4},\ \frac{1}{4}$$(v)$. $-3\frac{2}{7\ },\ -3\frac{4}{5}$
- Solve(a) \( \frac{2}{3}+\frac{1}{7} \)(b) \( \frac{3}{10}+\frac{7}{15} \)(c) \( \frac{4}{9}+\frac{2}{7} \)(d) \( \frac{5}{7}+\frac{1}{3} \)(e) \( \frac{2}{5}+\frac{1}{6} \)(f) \( \frac{4}{5}+\frac{2}{3} \)(g) \( \frac{3}{4}-\frac{1}{3} \)(h) \( \frac{5}{6}-\frac{1}{3} \)(i) \( \frac{2}{3}+\frac{3}{4}+\frac{1}{2} \)(j) \( \frac{1}{2}+\frac{1}{3}+\frac{1}{6} \)(k) \( 1 \frac{1}{3}+3 \frac{2}{3} \)(l) \( 4 \frac{2}{3}+3 \frac{1}{4} \)(m) \( \frac{16}{5}-\frac{7}{5} \)(n) \( \frac{4}{3}-\frac{1}{2} \)
- Name the property under multiplication used in each of the following.(i) \( \frac{-4}{5} \times 1=1 \times \frac{-4}{5}=-\frac{4}{5} \)(ii) \( -\frac{13}{17} \times \frac{-2}{7}=\frac{-2}{7} \times \frac{-13}{17} \)(iii) \( \frac{-19}{29} \times \frac{29}{-19}=1 \).
- Simpify the following :$(\frac{16}{17} of 6 \frac{4}{5}) -4 \frac{1}{5}-[1 \frac{1}{14} \div(\frac{1}{2}+\frac{1}{7})] $
- Find the sum of $\frac{1}{2}+\frac{1}{3}+\frac{1}{4}$.
- Simplify:\( 5 \frac{1}{4} \p 2 \frac{1}{3}-4 \frac{2}{3} \p 5 \frac{1}{3} \times 3 \frac{1}{2} \)
- Find the value of:$\left(\frac{3}{4}\ +\ \frac{1}{4}\right)\ \div\ 2\frac{1}{2}\ -\ \left(\frac{2}{3}\ \times\ \frac{7}{8}\right)\ \div\ 1\frac{1}{4}$
- Find the sum:$( \frac{4}{17}+\frac{19}{17})$
- \( 3+\frac{-1}{2}+\frac{-3}{4} \)
- Find the sum of two middle terms of the A.P.:$-\frac{4}{3}, -1, -\frac{2}{3}, -\frac{1}{3}, ......, 4\frac{1}{3}$.
- Add: $4 \frac{1}{2}+3 \frac{2}{4}$.
- Solve the following$ 9 \frac{3}{4} \div\left[2 \frac{1}{6}+\left\{4 \frac{1}{3}-\left(1 \frac{1}{2}+1 \frac{3}{4}\right)\right\}\right]$
- Simplify each of the following:$\frac{1}{3}$ of $1 \frac{1}{4}+2 \frac{1}{3}$
- Find:9th term of the A.P. $\frac{3}{4}, \frac{5}{4}, \frac{7}{4}, \frac{9}{4}, ………$
- Which of the following is greater?$\frac{1}{4} \times \frac{1}{4}$ or $\frac{1}{4} \times \frac{1}{7}$
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