2330 Working with sequences Several terms of a sequence an

23-30. Working with sequences Several terms of a sequence {an } n=1 are given. a. Find the next two terms of the sequence. b. Find a recurrence relation that generates the sequence (supply the initial value of the index and the first term of the sequence). c. Find an explicit formula for the general nth term of the sequence.

Solution

Solution:

a) Next two terms of the sequence are , 243 and 729 (as we notice that every next number is three times the current number)

b) Recurrence Relation,

=> a_n = 3(a_n-1) is the reccurrence relation, where a_0 = 1 and n = 1,2,3....... (here a_n represents next term and a_n-1 represents previous term)

c) Gerneral formula for finding nth term,

=> an (nth term) = 3^(n-1) where n can be a natural number.

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