6, 7, 16, 51, 208, Option 1) 1036 Option 2) 1042 Option 3) 1048 Option 4) 1056 Option 5) None of these
Question
6, 7, 16, 51, 208,
Option 1) 1036
Option 2) 1042
Option 3) 1048
Option 4) 1056
Option 5) None of these
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Answer
:
The correct option is E) None of these.
To identify the pattern in the given sequence:
$$ 6, 7, 16, 51, 208, \ldots $$
we apply the following operations:
-
Multiply by 1 and add 1: $$ 6 \times 1 + 1 = 7 $$
-
Multiply by 2 and add 2: $$ 7 \times 2 + 2 = 16 $$
-
Multiply by 3 and add 3: $$ 16 \times 3 + 3 = 51 $$
-
Multiply by 4 and add 4: $$ 51 \times 4 + 4 = 208 $$
Following this pattern, the next number would be:
- Multiply by 5 and add 5: $$ 208 \times 5 + 5 = 1045 $$
Therefore, none of the provided options match the calculated next term, thus the answer is E) None of these.
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