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Find the next two terms in the sequence: 1,3,7,15,31,.......

Question

Find the next two terms in the sequence:
$1, 3, 7, 15, 31, .......$

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Find the next two terms in the sequence:

1, 3, 7, 15, 31, .......

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Text solutionVerified

t_{1} = 1, t_{2} = 3, t_{3} = 7, t_{4} = 15, t_{5} = 31

t_{2} = 3 = 2 t_{1} + 1

t_{3} = 2 t_{2} + 1

t_{4} = 15 = 2 t_{3} + 1

∴

t_{n} = 2 t_{n - 1} + 1

t_{6} = 2 t_{5} + 1 = 2 \times 31 + 1 = 2 \times 31 + 1 = 62 + 1 = 63

t_{7} = 2 t_{6} + 1 = 2 \times 63 + 1 = 127

∴

The next two terms of the sequence are

63, 127

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Question Text	Find the next two terms in the sequence: $1, 3, 7, 15, 31, .......$
Answer Type	Text solution:1
Upvotes	150