Question

2, 7, 24, 59, 118, 207 what is the sequence after it and can anyone explain the pattern?

Answer 1

Answer:

Step-by-step explanation:

The series is a bit complex

$2=1^{3} -(-1)$

$7=2^{3} -1\\24=3^{3} -3\\59=4^{3} -5\\118=5^{3} -7\\207=6^{3} -9$

So the number which is to be subtracted increases by 2 and the number which we cube increases by 1

Hence, the next number would appropriately be

$7^{3} -11\\=343-11\\<u><strong>332</strong></u>(Ans).$

Answer 2

Given:

A sequence 2, 7, 24, 59, 118, 207.

To Find:

The logic between every term and the next term.

Solution:

The given problem can be solved by developing a common logic between every term

1. The first term is obtained using the logic,

=> 2 = $1^3 -(-1) = 1+1 = 2$,

2. The second term is obtained using the logic,

=> 7 = $2^3 - 1 = 7,$

3. The third term is obtained using the logic,

=> 24 = $3^3 - 3 = 24$,

4. The fourth term is obtained using the logic,

=> 59 = $4^3 - 5 = 59$,

5. The fifth term is obtained by using the logic,

=> 118 = $5^3 - 7 = 118$,

6. The sixth term is obtained by using the logic,

=>$207 = 6^3 - 9 = 207$,

• The common logic can be observed and the next term can be determined using the same logic,

7. The seventh term is obtained by using the same logic i.e,

=> Next term = $7^3 - 11 = 332.$

Therefore, the next term of the given sequence is 332.