If the {n^{th}} term of an A.P. be (2n - 1), | vedclass

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

Question

(c) Given that ${T_n} = 2n - 1$

First term $a = 2\ .\ 1 - 1 = 1$

Second term $b = 2\;.\;2 - 1 = 3$

Third term $c = 2\;.\;3 - 1 = 5$

Theref

Vedclass · Accepted Answer

${n^2}$

Vedclass · Answer

(c) Given that ${T_n} = 2n - 1$

First term $a = 2\ .\ 1 - 1 = 1$

Second term $b = 2\;.\;2 - 1 = 3$

Third term $c = 2\;.\;3 - 1 = 5$

Therefore sequence is $1,\;3,\;5,.......2n - 1$.

Now sum of the first $n$ terms is ${S_n} = \frac{n}{2}[a + l]$

$ = \frac{n}{2}[1 + 2n - 1] = \frac{n}{2}\;.\;2n = {n^2}$

Aliter : Since ${T_n} = 2n - 1$

$ \Rightarrow {S_n} = \Sigma {T_n} $

$= 2\Sigma n - \Sigma \;1 = n(n + 1) - n = {n^2}$

If the ${n^{th}}$ term of an $A.P.$ be $(2n - 1)$, then the sum of its first $n$ terms will be

Similar Questions

If ${n^{th}}$ terms of two $A.P.$'s are $3n + 8$ and $7n + 15$, then the ratio of their ${12^{th}}$ terms will be

Let $x _1, x _2 \ldots ., x _{100}$ be in an arithmetic progression, with $x _1=2$ and their mean equal to $200$ . If $y_i=i\left(x_i-i\right), 1 \leq i \leq 100$, then the mean of $y _1, y _2$, $y _{100}$ is

If $n$ arithmetic means are inserted between a and $100$ such that the ratio of the first mean to the last mean is $1: 7$ and $a+n=33$, then the value of $n$ is

The sides of a right angled triangle are in arithmetic progression. If the triangle has area $24$ , then what is the length of its smallest side ?

Maximum value of sum of arithmetic progression $50, 48, 46, 44 ........$ is :-