Question

the general term of a sequence is defined as An={n(n+3);n€N and s odd. ,n²+1;n€N is even find the fourth and seventh terms​

Answer 1

Step-by-step explanation:

Given :-

The general term of a sequence is defined as

i) { n( n+3);n ∈ N is odd}

ii) {n² +1 ; n ∈ N is even}

To find :-

fourth and seventh terms

Solution :-

Given that

The general term for an even number is n² +1 ; n ∈ N

We have, n = 4

Fourth term = 4²+1

=> Fourth term = 16+1

Therefore, Fourth term = 17

and

The gene term for an odd number is n(n+3) , n ∈N

We have , n = 7

Seventh number = 7(7+3)

=> Seventh term = 7(10)

=> Seventh term = 70

Therefore, Seventh term = 70

Answer :-

Fourth term of the sequence is 17

Seventh term of the sequence is 70

Answer 2

Sequence

Numbers belonging to a category is called Sequence. Each element in a sequence is called a term. Normally sequence will be written as $a_1,\:a_2,\:a_3..$

As we went through the concept about Sequence, Now, Let's move on finding the solution for our question.

Given :

• n(n+3) ; n € N and n is odd
• n²+1 ; n € N and n is even

We know that,

Fourth term (4th) would be even, and we use,

$\implies\sf{\:n^2\:+\:1}$ where n = even and n = 4

Substituting value in Formula, we get,

$\implies\sf{n^2\:+\:1}$

$\implies\sf{4^2\:+\:1}$

$\implies\sf{16\:+\:1}$

$\implies\sf{17}$

We also know that,

Seventh term (7th) would be odd, and we use,

$\implies\sf{n(n\:+\:3)}$ where n = odd and n = 7

Substituting value in Formula, we get,

$\implies\sf{n(n\:+\:3)}$

$\implies\sf{7(7\:+\:3)}$

$\implies\sf{7(10)}$

$\implies\sf{70}$

Hence,

• Fourth Term = 17 and
• Seventh Term = 70