Answer:
The 32nd term of Arithmetic sequence is -174
Step-by-step explanation:
Given: \(a_1=12, a_{13}=-60\)
We are given two term of the Arithmetic sequence.
Formula:
\(a_n=a+(n-1)d\)
For \(a_1=12\)
\(a=12\)
For \(a_{13}=-60\)
\(a+12d=-60\)
Using two equation solve for a and d
\(12+12d=-60\)
\(1+d=-5\)
\(d=-6\)
We need to find 32nd term
\(a_{32}=a+31d\)
\(a_{32}=12+31(-6)\)
\(a_{32}=12-186\)
\(a_{32}=-174\)
Hence, The 32nd term of Arithmetic sequence is -174
