Question

complete the series 16,22,42,84,156,?

Answer 1

• 16,22,42,84,156...... is the answer.....!!

Answer 2

Answer:

Concept:

Sequence:

• The terms of a sequence are added to form a series.
• A sequence in mathematics is a list of elements, usually numbers, where the significance of the order of the elements is important.
• Everything here fits neatly into a pre-established pattern.
• There are two kinds of sequence.
• A finite sequence of numbers is 10,20,30,40,50,60.
• An illustration of an infinite sequence is 3,6,9,...….

Given:

The series is $16,22,42,84,156,?$

To Find:

We need to find the missing number in the series.

Solution:

Let T1 represent the term 1, T2 represent the term 2, T3 represent the term 3, T4 represent the term 4, T5 represent the term 5, and T6 represent the term 6, respectively.

$T1=16$

$T2=22$

$T3=42$

$T4=84$

$T5=156$

$T6 = ?$

Lets find the difference between each terms,

$D1 = T2-T1 = 22-16=6$

$D2 = T3-T2 = 42-22=20$

$D3=T4-T3=84-42=42$

$D4=T5-T4=156-84=72$

If we see the difference, we can observe,

$D1=6$ can also be expressed as $2*3$

$D2=20$ can also be expressed as $4*5$

$D3=42$ can also be expressed as $6*7$

$D4=72$ can also be expressed as $8*9$,

Then,

$D5=110$ can also be expressed as $10*11$,

⇒  $D5=T6-T5$

⇒  $110=T6-156$

⇒  $110+156 = T6$

⇒  $266=T6$

The missing number in the series is $266$.

Therefore, the complete series will be $16,22,42,84,156,266$.

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