search
Log In
Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
0 votes
79 views

Find the value of the expression $1-6+2-7+3-8+\dots\dots$ to $100$ terms.

  1. $-250$
  2. $-500$
  3. $-450$
  4. $-300$
in Quantitative Aptitude 9.3k points 31 523 813
recategorized by
79 views

1 Answer

0 votes
$1-6+2-7+3-8+\cdots\  to\ 100\ terms$

$=\underbrace{1-6}_{-5}+\underbrace{2-7}_{-5}+\underbrace{3-8}_{-5}+\cdots +\underbrace{50-55}_{-5}$

$= (1+2+\cdots + 50) - (6+7+\cdots +55)$

$= (1+2+3+4+5)+\underbrace{(6+7+\cdots +50) - (6+7+\cdots +50)}_0-(51+52+53+54+55)$

$= (1+2+3+4+5)-(51+52+53+54+55) $

$=\cfrac{5}{2}\Bigl[2(1)+(5-1)(1)\Bigr] - \cfrac{5}{2}\Bigl[2(51)+(5-1)(1)\Bigr]$

$\left( \because Sum\ of\ n\ terms\ of\ A.P.\ sequence\ is,\  \cfrac{n}{2}\Bigl[2a+(n-1)d\Bigr]\right)$

$=\cfrac{5}{2}(6) - \cfrac{5}{2}(106)$

$=5(3)-5(53)$

$=15-265$

$=-250$
114 points 2 30 41
edited by

Related questions

0 votes
1 answer
1
102 views
The value of the following expression : $\left [ \frac{1}{2^{2}-1} \right ]+\left [ \frac{1}{4^{2}-1} \right ]+\left [ \frac{1}{6^{2}-1} \right ]+\dots\dots+\left [ \frac{1}{20^{2}-1} \right ]$ is : $\frac{10}{21}$ $\frac{13}{27}$ $\frac{15}{22}$ $\frac{22}{15}$
asked Apr 3, 2020 in Quantitative Aptitude Lakshman Patel RJIT 9.3k points 31 523 813 102 views
0 votes
1 answer
2
71 views
The sum of first $n$ terms of an $A.P$. whose first term is $\pi$ is zero. The sum of next $m$ terms is : $\frac{ \pi m \left(m+n \right)}{n-1}$ $\frac{ \pi n \left(m+n \right)}{1-n}$ $\frac{ \pi m \left(m+n \right)}{1-n}$ $1$
asked Apr 3, 2020 in Quantitative Aptitude Lakshman Patel RJIT 9.3k points 31 523 813 71 views
0 votes
0 answers
3
92 views
The greatest number of four digits which is divisible by each one of the numbers $12$, $18$, $21$ & $28$, is : $9848$ $9864$ $9828$ $9636$
asked Apr 3, 2020 in Quantitative Aptitude Lakshman Patel RJIT 9.3k points 31 523 813 92 views
1 vote
1 answer
4
100 views
Of the three numbers, the sum of the first two is $45$; the sum of the second and third is $55$ and the sum of the third and thrice the first is $90$. The third number is : $20$ $25$ $30$ $35$
asked Apr 3, 2020 in Quantitative Aptitude Lakshman Patel RJIT 9.3k points 31 523 813 100 views
1 vote
0 answers
5
80 views
Study the following information carefully to answer the questions given below: A number sorting machine when given an input of numbers, rearranges the numbers in a particular manner step by step as indicated below till all the numbers are arranged in a particular order. Given below is an illustration of this ... $\text{17 24 47 62 92 86 42 79}$ $\text{17 47 62 86 24 42 79 92}$
asked Apr 3, 2020 in Logical Reasoning Lakshman Patel RJIT 9.3k points 31 523 813 80 views
...