The fifth term of an arithmetic sequence is 9 and the 32nd term is -84. What is the 23rd term?
an=a1+(n−1)da5=a1+4d=9a32=a1+31d=−84subtract a5 from a3227d=−93d=−9327=−319a1=9−4d=9−4(−319)=9+1249=2059a23=a1+22d=2059+22(−319)=−53
.The fifth term of an arithmetic sequence is 9 and the 32nd term is -84.
What is the 23rd term?
Formula of an arithmetic sequence:
|aiajakijk111|=0ai(j−k)+aj(k−i)+ak(i−j)=0
Set i=5, j=32, k=23 Set ai=a5=9, aj=a32=−84, ak=a23
ai(j−k)+aj(k−i)+ak(i−j)=09(32−23)+(−84)(23−5)+a23(5−32)=09(9)+(−84)(18)−a23(27)=081−1512−27a23=027a23=81−151227a23=−1431a23=−143127a23=−53