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

Answer:

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

Step-by-step 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:

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