Several terms of a sequence {a_n}_(n=1)^oo are given. a. Find the next two terms of the sequence. b. Find a recurrence relation that generates the seq

Amari Flowers 2020-12-05 Answered

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 nth term of the sequence. {1, 3, 9, 27, 81, ...}

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pivonie8
Answered 2020-12-06 Author has 91 answers
Concept Used- nth term of the geometric sequence is given by,
Tn=a+(n1)d, where a is the first term and d is the common ratio.
a) The new term of sequence can be find out by multiplying previous term by 3.
So, the next two terms are 243, 729.
b) For recurrence relation, we can write as,
a1=1
an+1=3an
c) As the nth term for the sequence (a,ar,ar2,ar3,.) is Tn=a·rn1, where a is the first term and r is the common ratio that can be find out by r=T2T1=T3T2=T4T3=
Now, for the sequence given {1,3,9,27,81,.}, we can write as,
Tn=1·3n1
Tn=3n1
Answer
(a) Hence, the next two terms are 243,729.
(b) The recurrence relation is an+1=3an.
(c) And explicit formula for the nth term of the sequence is Tn=3n1.
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