Let a sequence be defined by a1- 0 and an-1- an-4n-3 for all n- 1 n- NThe value of ak in terms of k is k- N

The correct option is A (k 1)(2k+3) a _ n+1 = a _ n +4n+3 a _ 2 = a _ 1 +4.1+3=7=( 2 1 ) ( 2 · 2+3 ) a _ 3 = a _ 2 +4.2+3=18=( 3 1 ) ( 3 · ...

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Standard XII

Mathematics

Summation by Sigma Method

Let a sequenc...

Question

Let a sequence be defined by $a_{1} = 0$ and $a_{n + 1} = a_{n} + 4 n + 3$ for all $n \geq 1 (n ϵ N)$

The value of $a_{k}$ in terms of k is $(k \in N)$

(k - 1) (2 k + 3)

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(k - 1) (3 k + 1)

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(k - 1) (k + 3)

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(k - 1) (2 k + 5)

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Solution

The correct option is A $(k - 1) (2 k + 3)$
$a_{n + 1} = a_{n} + 4 n + 3$

$a_{2} = a_{1} + 4.1 + 3 = 7 = (2 - 1) (2 \cdot 2 + 3)$

$a_{3} = a_{2} + 4.2 + 3 = 18 = (3 - 1) (3 \cdot 2 + 3)$

$a_{k} = (k - 1) (2 k + 3)$

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Q. Let

C_{k} =

^{n} C_{k}

for

0 \leq k \leq n

and

A_{k} = [\begin{matrix} C_{k - 1}^{2} & 0 0 & C_{k}^{2} \end{matrix}]

for

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, then

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Let a sequence be defined by a1=0 and an+1=an+4n+3 for all n≥1(nϵN)The value of ak in terms of k is (k∈N)

The correct option is A (k−1)(2k+3)an+1=an+4n+3a2=a1+4.1+3=7=(2−1)(2⋅2+3)a3=a2+4.2+3=18=(3−1)(3⋅2+3)ak=(k−1)(2k+3)

Let a sequence be defined by $a_{1} = 0$ and $a_{n + 1} = a_{n} + 4 n + 3$ for all $n \geq 1 (n ϵ N)$

The value of $a_{k}$ in terms of k is $(k \in N)$

The correct option is A $(k - 1) (2 k + 3)$
$a_{n + 1} = a_{n} + 4 n + 3$

$a_{2} = a_{1} + 4.1 + 3 = 7 = (2 - 1) (2 \cdot 2 + 3)$

$a_{3} = a_{2} + 4.2 + 3 = 18 = (3 - 1) (3 \cdot 2 + 3)$

$a_{k} = (k - 1) (2 k + 3)$