Answer:
The 32nd term of arithmetic sequence is -374.
Step-by-step explanation:
Given : the arithmetic sequence where \(a_1 = -33\) and \(a_{9} =-121\)
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 \(a_n=a+(n-1)d\)
Thus, for the given arithmetic sequence, we have,
First term is -33
\(a_{9}=a+(9-1)d=-121\)
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\(a_n=a+(n-1)d\)
We have,
\(a_{32}=-33+(32-1)(-11)\)
Simplify, we have,
\(a_{32}=-33+(31)(-11)\)
\(a_{32}=-33-341=-374\)
\(a_{32}=-374\)
Thus, the 32nd term of arithmetic sequence is -374.
