Question : What is the value of the expression $1-7+2-8+3-9+4-10+\ldots \ldots$ to 100 terms?
Option 1: – 200
Option 2: – 360
Option 3: – 300
Option 4: – 240
New: SSC CHSL Tier 2 answer key released | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
Correct Answer: – 300
Solution :
The given expression alternates between adding and subtracting the numbers 1, 7, 2, 8, 3, 9, 4, 10, and so on.
We can observe that the numbers being added increase by 1 each time, while the numbers being subtracted also increase by 1 each time.
To find the value of the expression to 100 terms, group the terms into pairs.
Each pair consists of a positive number and its negative counterpart.
The sum of each pair is always – 6 because (–7 + 1 = – 6, – 8 + 2 = – 6, – 9 + 3 = – 6, and so on).
Since we have 100 terms in total, we can form 50 pairs.
Each pair sums up to – 6, so the sum of the 100 terms is = 50 pairs × (–6) = –300
$\therefore$ The value of the expression 1 – 7 + 2 – 8 + 3 – 9 + 4 – 10 + ... to 100 terms is – 300.
Hence, the correct answer is – 300.
Related Questions
Know More about
Staff Selection Commission Combined High ...
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Get Updates Brochure
Your Staff Selection Commission Combined Higher Secondary Level Exam brochure has been successfully mailed to your registered email id “”.
