Question

For an arithmetic sequence, the common difference is 4 and the 38th term is 141. What is the value of the 5th term?

Answer 1

an = a1 +d(n-1)

141 = a1 + 4 (38-1)

141 = a1 +4*37

141=a1+148

a1 = -7

an =a1+d(n-1)

a5 = -7 +4(4)

a5 = -7 +16

a5 =9

Answer 2

$a_n=a_1+(n-1)d\\\\a_{38}=a_1+(38-1)d=a_1+37d\\\\a_{38}=141,\ d=4.\\\\Substitute:\\\\141=a_1+37(4)\\\\141=a_1+148\qquad|-148\\\\a_1=-7\\\\a_5=a_1+(5-1)d=a_1+4d\\\\Substitute:\\\\a_5=-7+4(4)=-7+16=9\\\\Answer:\ 5th\ term = 9$