Answer:
The 32nd term of arithmetic sequence is -374.
Step-by-step explanation:
Given : the arithmetic sequence where [tex]a_1 = -33[/tex] and [tex]a_{9} =-121[/tex]
We have to find the 32nd term of the arithmetic sequence.
For the arithmetic sequence having first term 'a' and common difference 'd' the general term is defined by [tex]a_n=a+(n-1)d[/tex]
Thus, for the given arithmetic sequence, we have,
First term is -33
[tex]a_{9}=a+(9-1)d=-121[/tex]
We can calculate the common difference by putting a = -33 in above, we have,
-33 + 8 d = -121
Solving for d, we have,
8d = -121 + 33
⇒ 8d = -88
⇒ d = - 11
Thus, the common difference is -11.
For 32nd term, Put a = -33 , d = -11 and n = 32 in[tex]a_n=a+(n-1)d[/tex]
We have,
[tex]a_{32}=-33+(32-1)(-11)[/tex]
Simplify, we have,
[tex]a_{32}=-33+(31)(-11)[/tex]
[tex]a_{32}=-33-341=-374[/tex]
[tex]a_{32}=-374[/tex]
Thus, the 32nd term of arithmetic sequence is -374.
