Question

What is the missing number in the series 7 10 15 17 23 24 31 _ 39 ?
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Answer 1

Answer:

Of course, the answer will be: 31

Let me explain:

Observe the sequence plainly. The series is increasing by following this pattern below:

(2nd number - 1st number)+ 2 + 2nd number = 3rd number

(3rd number - 2nd number) + 2 + 3rd number = 4th number

……………………………………….

……………………………………….

Applying this pattern, you can easily determine the next number of this series.

Now, I’m going to apply the pattern:

> (10–7)+2+10 = 15

>(15–10) + 2 + 15 = 22

> (22–15)+2+22 = 31

You can also determine the next number by following this pattern from bellow. It’s easier !

The first number of this series is 7

The second number is, 7+3 = 10

The third number is, 10+5=15

The 4th number is, 15+7=22

Look! the series is increasing by means of adding the odd number gradually… where the odd starts from 3…

Then the next number will be, 22+9=31…..

Another theory you can apply: => a+(a+3)+(a+3+5)+(a+3+5+7)+(a+3+5+7+9)+(a+3+5+7+9+11)+(a+3+5+7+9+11+13)+………….

Here, “a” is the first number of the series!

Have a nice journey in MATHEMATICS !! :)

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Answer 2

Answer: The missing number is 31

Step-by-step explanation:

The given series follows two different patterns.

Odd position numbers            Even position numbers

     7                                                       10

     15                                                     17

     23                                                    24

     31                                                      ?

     39

The numbers at odd positions are in AP with common difference 8.

The numbers at even position are in AP with common difference 7.

nth term (Tₙ) of an AP with first term a and common difference d is given by the formula :

$T_n = a + (n-1)d$

For even positioned numbers :

a = 10

d = 7

We have to find the 4th even positioned number. Hence, n = 4

$T_n = a + (n-1)d$

⇒ $T_4 = a + (4-1)d$

⇒ $T_4 = a + 3d$

⇒ $T_4 = 10 + 3(7)$

⇒ $T_4 = 10 +21$

⇒ $T_4 = 31$

Hence, the missing number is 31.

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