Given that \(1+2+3+\ldots+9=45\), find the value of \(11+12+13+\ldots+19\).
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 135
Each of 11, 12, …, 19 is 10 more than the matching number 1, 2, …, 9, so the new sum is the given sum plus nine tens.
\(11+12+\ldots+19=(1+10)+(2+10)+\ldots+(9+10)\)
\(=45+9\times10=45+90=135\)
The sum is 135.