Question

Given a sequence is defined by a first term of LaTeX: t_1=3t 1 = 3, and explicit definition LaTeX: t_n=\:4n-1t n = 4 n − 1, find the 4th term of the sequence (i.e. LaTeX: t_4t 4).

Group of answer choices


3


11


15


171


Which sequence could be described by the explicit definition: LaTeX: a_n=n^2-5a n = n 2 − 5

Group of answer choices


1,-4,4,11,116,...


1,2,3,4,5,6,...


-4,-1,4,11,20,....


-4,11,116,13451

Answer 1

`1) 15\: 2)(-4,-1,11,20,...)`

Explanation:

1) To find the 4th term given the Explicit Formula, i.e. definition, just plug it in. The common difference according to question is 4, the 1st term is 3.

`t_(1)=3\\t_(n)=t_(1)+4(n-1)\\t_(n)=t_(1)+(n-1)d\\t_(4)=3+4(3)\\t_(4)=15`

2) For this another Sequence in Explicit definition we just need to plug it in:

`a_(n)=n^(2)-5\\a_(1)=1^(2)-5 \Rightarrow a_(1)=-4\\a_(2)=2^(2)-5\Rightarrow a_(2)=-1\\a_(3)=3^(2)-5\Rightarrow a_(3)=4\\a_(4)=4^(2)-5\Rightarrow a_(4)=11\\a_(5)=5^(2)-5\Rightarrow a_(5)=20\\(-4,-1,11,20,...)`