Respuesta :
Answer:
The 32nd term of the arithmetic sequence is -386.
Step-by-step explanation:
Given: The arithmetic sequence where [tex]a_1=-34[/tex] and [tex]a_9=-122[/tex]
We have to find the 32nd term of the arithmetic sequence.
Consider the given sequence with [tex]a_1=-34[/tex] and [tex]a_9=-122[/tex]
We know , For a given sequence in an Arithmetic sequence with first term [tex]a_1[/tex] and common difference d , we have,
[tex]a_n=a_1+(n-1)d[/tex]
We first find the common difference "d".
[tex]a_9=-122[/tex]
[tex]a_9=a_1+(9-1)d[/tex]
[tex]a_1=-34[/tex] , we have,
[tex]-122=-34+8d[/tex]
Solve for d , we have,
-88= 8d
d = - 11
Thus, 32nd term is [tex]a_{32}=a_1+(32-1)d[/tex]
[tex]a_{32}=-34+32\cdot (-11)[/tex]
[tex]a_{32}=-386[/tex]
Thus, The 32nd term of the arithmetic sequence is -386.
