Find a formula for the general term ⍺n of the sequence?
Find a formula for the general term ⍺n of the sequence, assuming that the pattern of the first few terms continues.
{-7, 14/3, -28/9, 56/27, -112/81, ...}
Find a formula for the general term ⍺n of the sequence, assuming that the pattern of the first few terms continues.
{-7, 14/3, -28/9, 56/27, -112/81, ...}
1 Answer
Explanation:
In the given sequence, we observe that
-
Starting from first term which is negative, next term is positive and then third term is again negative and this goes on. Hence we can write it as
#(-1)^n# . -
Numertors in sequence are
#{7,14,28,56,112,.......}# and as it is a geometric sequence with first term as#7# and common ratio#2# . Hence#n^(th)# term is#7xx2^(n-1)# . -
Denominators in sequence are
#{1,3,9,27,81,........}# again a geometric sequence with first term as#1# and common ratio#3# . Hence#n^(th)# term is#1xx3^(n-1)=3^(n-1)# .
Hence