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We have been given the sequence 2,3,5,9,17.
We can write the terms of this sequence as
From the above term we can see that for the first term we take exponent 0 on 2 and then add 1 .
For second term we take exponent 1 on 2 and then add 1 .
For third term we take exponent 2 on 2 and then add 1 .
Using this fact for the next term of the sequence i.e. 6th term, we can take exponent 5 on 2 and then add 1 .
Therefore, next term of the sequence is given by
Therefore, the next term is 33.
Using the above facts, the pattern is given by
C
generate the first few terms using the recursive formula
= - 7 ×
= -
= -
×
= -
= -
×
= -
r = /
=
the n th term formula (explicit ) for a geometric sequence is
=
= - 7(
)^(n - 1)