How many terms are there in the sequence 1, 3 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The given sequence is $1, 3, 6, 10, 15, 21, \dots, 5050$.These are triangular numbers,where the $n$-th term is given by the formula $T_n = \frac{n

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(B) The given sequence is $1, 3, 6, 10, 15, 21, \dots, 5050$.These are triangular numbers,where the $n$-th term is given by the formula $T_n = \frac{n(n+1)}{2}$.We are given that the last term $T_n = 5050$.So,$\frac{n(n+1)}{2} = 5050$.$n(n+1) = 10100$.$n^2 + n - 10100 = 0$.Solving this quadratic equation using the quadratic formula $n = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$:$n = \frac{-1 \pm \sqrt{1^2 - 4(1)(-10100)}}{2(1)} = \frac{-1 \pm \sqrt{1 + 40400}}{2} = \frac{-1 \pm \sqrt{40401}}{2}$.Since $\sqrt{40401} = 201$,we have $n = \frac{-1 + 201}{2} = \frac{200}{2} = 100$.Thus,there are $100$ terms in the sequence.

How many terms are there in the sequence $1, 3, 6, 10, 15, 21, \dots, 5050$?

Similar Questions

For any integer $n \geq 1$,the sum $\sum_{k=1}^n k(k+2)$ is equal to

$\frac{1}{2 \cdot 5} + \frac{1}{5 \cdot 8} + \frac{1}{8 \cdot 11} + \ldots$ to $16$ terms $=$

For all positive integral values of $n$,the value of $3 \cdot 1 \cdot 2 + 3 \cdot 2 \cdot 3 + 3 \cdot 3 \cdot 4 + \dots + 3 \cdot n \cdot (n + 1)$ is

$1 + (1 + a)x + (1 + a + a^2)x^2 + \dots \infty = \dots \, (0 < a, x < 1)$

What is the sum of $n$ terms of the series $2 + 5 + 14 + 41 + \dots$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module