Question

CW: If the 5th term and the 10th term of an arithmetic

sequence is 44 and 89 respectively, what is the value of the
21st term? (show your work for a full mark)

Answer 1

a₂₁ = 188

Explanation:

The n-th term of an arithmetic sequence:
`a_n=a_1+d(n-1)`

so:

`a_5=a_1+d(5-1)\\a_5=a_1+4d\\a_1=a_5-4d\\a_1=44-4d\\\\a_(10)=a_1+d(10-1)\\ a_(10)=a_1+9d\\89=44-4d+9d\\45=5d\\d=9\\\\a_1=44-4\cdot9 = 8\\\\a_(21)=a_1+ 20d=8+20\cdot9=188`