Answer:
\(a_{32}=-173\)
Step-by-step explanation:
Given : the arithmetic sequence where\(a_1 = 13\) and \(a_{13} =-59\)
We have to find the 32nd term of the arithmetic sequence.
Since, the general arithmetic sequence having first term 'a' and common difference 'd' is given by \(a_n=a+(n-1)d\)
Thus, for the given arithmetic sequence, we have,
First term is \(a_1=a= 13\) and
\(a_{13}=a+(13-1)d=-59\)
Calculate the common difference by putting a = 13 in above, we have,
\(13+(12)d=-59\)
Solving for d, we have,
\((12)d=-59-13\)
\((12)d=-72\)
Divide by 12 both side, we have,
\(d=-6\)
Thus, the common difference is -6.
For 32nd term, Put a = 13 , d = -6 and n = 32 in \(a_n=a+(n-1)d\)
We have,
\(a_{32}=13+(32-1)(-6)\)
Simplify, we have,
\(a_{32}=13+(31)(-6)\)
\(a_{32}=13-186\)
\(a_{32}=-173\)
