Question

1, 5, 10, 27, 58, 153, 340 ?
​

Answer 1

The given sequence:

1, 5, 10, 27, 58, 153, 340, ?

We have to find, the value of missing number(?).

Solution:

10 = 5 + (4 × 2 - 3 )

    = 5 + (8 - 3 = 5) = 10

27 = 10 + (5 × 3 + 2)

    = 10 + (15 + 2 = 17) = 10

58 = 27 + (17 × 2 - 3 )

    = 27 + (34 - 3 = 31) = 58

153 = 58 + (31 × 3 + 2)

    = 58 + (93 + 2 = 95) = 153

340 = 153 + (95 × 2 - 3 )

    = 153 + (190 - 3 = 187) = 340

Similarly:

? = 340 + (187 × 3 + 2)

⇒ ? = 340 + 561 + 2

⇒ ? = 340 + 563

⇒ ? = 903

∴ Missing number (?) = 903

Answer 2

Given : 1, 5, 10, 27, 58, 153, 340, ?​

To Find :  Missing number

Solution:

1,    5,     10,    27,     58,      153,     340,     (? = 340 + x)

  4     5       17      31       95        187        x

Sequence of Differences

4

5  = 4 x 2  - 3

17 = 5 x 3  + 2

31 = 17 x 2 - 3

95 = 31 x 3 + 2

187 = 95 x 2 - 3

x = 187 x 3 + 2

=> x = 561 + 2

=> x = 563

alternate Sequence    x 2 -  3   and  x 3  + 3

? = 340 + x

= 340 + 563

= 903

missing number is 903

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