Question

HELP HELP HELP .
Identify the 27th term of an arithmetic sequence where a1 = 38 and a17 = -74. (2 points)
Answer

-20.5

-151

-22.75

-144


Identify the 35th term of an arithmetic sequence where a1 = -7 and a18 = 95. (2 points)
Answer

203

197

168

163

Answer 1

Do you know this equation \[a_{n}=a_{1}+(n-1).r\] all right? So, first question:
\[a_{17}=a_{1}+(17-1).r \rightarrow -74 = 38 + 16.r \rightarrow 16.r=-112 \] and r = -7

Answer 2

So, \[a_{27}=38+(27-1).(-7) \rightarrow a_{27} = 38 - 182 \rightarrow a_{27} = -144\]

Answer 3

Use the same equation to resolve second question:
\[a_{18}=a_{1}+(18-1).r \rightarrow 95 = -7 + 17r \rightarrow 102 = 17r \rightarrow r=6\] and.....
\[a_{35}=-7+(35-1).6 \rightarrow a_{35} = -7 + 204 \rightarrow a_{35} = 197\]