Question

6, 35, 143, 323
a) 646 b) 667
c) 632 d) 969

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Answer 1

We can observe a pattern here that numbers are only multiplied by prime numbers:

$& 2\times 3=6 \\ & 3\times 5=15 \\ & 5\times 7=35 \\ & 7\times 11=77 \\ & 11\times 13=143 \\ & \text{Similarly,} \\ & 17\times 19=323 \\ & 23\times 29=667$

Therefore, (b) is the correct option.

Answer 2

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers.

Given:

The given series are $6,35,143,323$

In this next series the pattern followed is:

The term of the series are products of two consecutive prime number i.e.,

$2\times3=6\\5\times7=35\\11\times13=143\\17\times19=323\\23\times29=667$

So the next series is $667.$a