Question

28,6,36,15,1,10,21,3,?​

Answer 1

Solution:

This is a sequence of a Triangular Series.

The correct triangular series is:

→ 1, 3, 6, 10, 15, 21, 28, 36, ?

If we analyse the difference between each consecutive number we get a pattern of natural numbers.

→ 1 + 2 = 3

→ 3 + 3 = 6

→ 6 + 4 = 9

→ 10 + 5 = 15

→ 15 + 6 = 21

→ 21 + 7 = 28

→ 28 + 8 = 36

Therefore the next number is written as:

→ 36 + 9 = 45

Hence the required number is 45.

Alternative Method:

The general term of a Triangular series is given as:

$\boxed{ x_n = \dfrac{n(n+1)}{2}}$

According to the question, the question mark is in the 9th position. Hence substituting 'n' as 9, we get:

$\rightarrow x_9 = \dfrac{ 9 ( 9 + 1)}{2}\\\\\rightarrow x_9 = \dfrac{9\times10}{2}\\\\\rightarrow \boxed{x_9 = \dfrac{90}{2} = 45}$

Hence 45 is the required number.

Answer 2

Given: $28,6,36,15,1,10,21,3,?$

To Find: What is the $9^{th}$ position value.

Step-by-step explanation:

$28,6,36,15,1,10,21,3,?$

Lets the sequence is,

$1, 3, 6, 10, 15, 21, 28, 36, ?$

We know the Triangular Series for the $n^{th}$ terms is,

$T_{n}=\frac{n(n+1)}{2}$

From the question, the question marks at $9^{th}$,

So, $n=9$

∴ $T_{9}=\frac{9(9+1)}{2}$

⇒$T_{9}=\frac{9\times 10}{2}$

⇒$T_{9}=\frac{90}{2}$

∴$T_{9}=45$

So, The Answer is $45$