Which will come in the blank space ?
7,26,63,124,_____,342,511.
Answers
Given: 7, 26, 63, 124, ___, 342, 511
To Find: The missing number.
Solution: Let's start by multiplying, adding and subtracting to get the resultant number.
We can write 7 as the product of 2 and 3 & later can add 1 to get te resultant. Let's apply the same on others too. 26 can be written as the product of 5 and 5 & later add 1 in it. Whereas 63 can be written as the product of 8 and 8 & later subtract 1 from it.
In first two numbers we add one while in the thrid one we subtract one from it. (It's clear that we can't apply this rule).
Take the third number again i.e. 63 which is the perfect cube of 4 and later 1 is subtracted from it.
→ 4³ - 1 = 64 - 1 = 63
Similarly,
→ 2³ - 1 = 8 - 1 = 7
→ 3³ - 1 = 27 - 1 = 26
→ 4³ - 1 = 64 - 1 = 63
→ 5³ - 1 = 125 - 1 = 124
From above it's clear that each time cube is increasing by one and later one is decreased.
Therefore, missing number is the cube of 6 and later one is subtracted from it.
→ 6³ - 1 = 216 - 1 = 215
Let's check the rest numbers too, by applying the same rule.
→ 7³ - 1 = 343 - 1 = 342
→ 8³ - 1 = 512 - 1 = 512
Therefore, the missing number is 215.