## Number Puzzle #180

What will be the next number in this series?

1 , 17 , 98 , 354 , ?

What will be the next number in this series?

1 , 17 , 98 , 354 , ?

-1¹²¹ -1¹²² -1¹²³ -1¹²^⁴ =?

Check your answer:-

Click here to See Solution
-1^n is 1 (if n is even) OR -1 (in n is odd)

but in this equation power is on 1 not -1

-1¹²¹-1¹²² -1¹²³-1¹²^⁴ = -1-1-1-1 = -4

What will be the next number in this series?

11,15,19,18,26,21,32, 24,37,____

If 1*36=36

8*23=23

8*67=1

Then

9*10=?

0, 1, 5, 19, 65, 211, ?

Check your answer:-

Answer: 665

explanation:

it follows this equation** 3^n – 2^n** where n is integer starting from 0

explanation:

it follows this equation

thus

3^0 – 2^0 = 1 – 1 = 0

3^1 – 2^1 = 3 – 2 = 1

3^2 – 2^2 = 9 – 4 = 5

3^3 – 2^3 = 27 – 8 = 19

3^4 – 2^4 = 65

3^5 – 2^5 = 211

3^6 – 2^6 = 729 – 64 = 665

There is one more way to solve this

**3*previous number + 2^(n-1)**

0x3+1=1;

1×3+2=5;

5×3+4=19;

19×3+8=65;

65×3+16=211;

211×3+32=665;

**wondering how it is possible?**

lets solve 3*previous number + 2^(n-1)

=> 3*(3^(n-1) – 2^(n-1)) + 2^(n-1)

=> 3^n – (2+1)*2^(n-1) + 2^(n-1)

=> 3^n – 2^n – 2^(n-1) + 2^(n-1)

=> 3^n – 2^n i.e. our first equation

Number Puzzle #175

find out the missing number

2 3 1 2

3 4 4 5

5 6 6 7

30 43 51 ?

2 6 18

4 20 100

X 21 147

find X

Check your answer:-

in first row next number is a multiplication of 3 and the previous number

second row, next number is a multiplication of 5 and the previous number

in third row 3rd number (147) is a multiplication of 7 and previous number, i.e. 21, thus X*7 = 21 =>

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