Question

find the missing term. 10,55,145,325,685,?​

Answer 1

ANSWER:

Given:

• 10, 55, 145, 325, 685, ?

To Find:

• Missing number

Solution:

Let the missing number be x.

So, the series is:

⟹ 10, 55, 145, 325, 685, x.

There can be 2 methods to solve this.

METHOD 1:

(Taking Difference)

Now, as the method says, we will take difference of the terms and try to make a pattern of it.

So, the differences pf consecutive terms are:

• 10, 55 = 55 - 10 = 45
• 55, 145 = 145 - 55 = 90
• 145, 325 = 325 - 145 = 180
• 325, 685 = 685 - 325 = 360
• 685, x = x - 685

So, the differences are:

⟹ 45, 90, 180, 360, (x - 680)

We can see that,

• 45 = 45 × 1
• 90 = 45 × 2
• 180 = 45 × 4
• 360 = 45 × 8

We can see that, the differences have a fixed pattern.

⟹ 1, 2, 4, 8

We can rewrite it as,

⟹ 2^0, 2^1, 2^2, 2^3

Therefore, the next will be 2^4 = 16.

Just as,

⟹ 360 = 45 × 2^3

Similarly,

⟹ x - 685 = 45 × 2^4

⟹ x - 685 = 45 × 16

⟹ x - 685 = 720

Therefore,

⟹ x = 720 + 685

⟹ x = 1405.

Therefore, the missing number is 1405.

METHOD 2:

In this method, we will rewrite the terms, so that they make a fixed pattern instead of finding pattern in the differences of consecutive terms.

So,

⟹ 10, 55, 145, 325, 685, x.

Now, we can rewrite them as,

• 55 = (10 × 2) + 35 [20 + 35 = 55]
• 145 = (55 × 2) + 35 [110 + 35 = 145]
• 325 = (145 × 2) + 35 [290 + 35 = 325]
• 685 = (325 × 2) + 35 [650 + 35 = 685]

So, we can see that the pattern is:

⟹ (previous term × 2) + 35

So,

⟹ x = (685 × 2) + 35

⟹ x = 1370 + 35

⟹ x = 1405.

Therefore, the missing number is 1405.