Question

1, 4, 15, 47, 120, 261, ?​

Answer 1

Given :- 1, 4, 15, 47, 120, 261, ?

Solution :-

Look at the difference between terms we get,

→ 4 - 1 = 3

→ 15 - 4 = 11

→ 47 - 15 = 32

→ 120 - 47 = 73

→ 261 - 120 = 141

Now, again checking difference between difference terms we get ,

→ 11 - 3 = 8

→ 32 - 11 = 21

→ 73 - 32 = 41

→ 141 - 73 = 68

again checking difference between difference terms we get ,

→ 21 - 8 = 13

→ 41 - 21 = 20

→ 68 - 41 = 27

Finally, again checking difference between difference terms we get ,

→ 20 - 13 = 7

→ 27 - 20 = 7 .

therefore,

→ Next difference will be = 27 + 7 = 34

→ Next difference will be = 68 + 34 = 102

→ Next difference will be = 141 + 102 = 243

finally,

→ Next term will be = 261 + 243 = 504 (Ans.)

Hence, Next term in the series will be 504.

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