**Determine the number of terms in the arithmetic sequence below.**\(-30, -29, -28, \ldots, 77, 78, 79, 80\)The number of terms in the sequence \(-30, -29, -28, \ldots, 77, 78, 79, 80\) is \[ \Box \]*Enter your answer in the answer box.*

Name: **Determine the number of terms in the arithmetic sequence below.**\(
Uploaded: 2024-03-20T06:38:58.000Z
Channel: Bartleby
Description: **Determine the number of terms in the arithmetic sequence below.**\(-30, -29, -28, \ldots, 77, 78, 79, 80\)The number of terms in the sequence \(-30, -29, -28, \ldots, 77, 78, 79, 80\) is \[ \Box \]*Enter your answer in the answer box.*

Given: Arithmetic sequence, -30.-29,-28,...,77,78,79,80Explanation: To determine the terms in the arithmetic sequence use formula given below, an=a+(n-1)dsolve for n,an-a=(n-1)dan-ad=n-1an-ad+1=nwhere,n=Total number of termsan=final term / last terma=initial term / first termd=common difference a2-a1Since according to arithmetic sequence First term (a)=-30 Final term an=80 Common difference (d)=a2-a1 d=-29-(-30)=-29+30=1Now put all above values in the formula,Therefore,n=an-ad+1n=80-(-30)1+1n=80+30+1n=110+1n=111Therefore there are total 111 termsThe number of terms in the sequence -30,-29,...,79,80 is 111. Hence the solution.