Question

What will be the general formula for the given number pattern ?

1 , 4 , 9 , 16 , 25 , 36 , _ _ _ _

(a) n + n (b) n × n

(c) n ÷ n (d) n – n​

Answer 1

Given :

What will be the general formula for the given number pattern ?  

1 , 4 , 9 , 16 , 25 , 36 , _ _ _ _

Options :

a. n + n

b. n × n

c. n ÷ n

d. n - n

Solution :

1 , 4 , 9 , 16 , 25 , 36 , ...

• 1 will be written as 1²
• 4 will be written as 2²
• 9 will be written as 3²
• 16 will be written as 4²
• 25 will be written as 5²
• 36 will be written as 6²

.

.

.... n²

➠ 1² , 2² , 3² , 4² , 5² , 6² , ... , n²

So , general formula will be n²  $\orange{\bigstar}$

where ,

• n denotes natural number
• n = 1 , 2 , 3 , .......

General formula is  n²

➠ n × n

Option (b)

More Info :

Given series is ' squares of natural numbers '

General formula for

• 1 , 9 , 25 , 49 , ...  

➠ 1² , 3² , 5² , 7² , ... (2n-1)²

➠ (2n - 1 )² is general formula

where ,

• n denotes natural number

Answer 2

Answer:

• Option (B) n × n

Explanation:

Given that,

• 1 , 4 , 9 , 16 , 25 , 36,......

So, general formula will be n² $\purple\bigstar$

Here,

• n = Natural number

↪ General formula = n²

↪ General formula = n × n $\red\bigstar$

For information:

• Defination: Natural numbers are the numbers which are positive integers and includes numbers from 1 till infinity(∞). These numbers are countable and are generally used for calculation purpose. The set of natural numbers is represented by the letter “N”. N = {1,2,3,4,5,6,7,8,9,10…….}

• According to the Ramanujan ; Sum of natural numbers will be 1 , 2 , 3 , 4 , ..... = -1/12