contestada

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)

Respuesta :

unicorn3125

Answer:

         a₂₁ = 188

Step-by-step explanation:

The n-th term of an arithmetic sequence:  [tex]a_n=a_1+d(n-1)[/tex]

so:

    [tex]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[/tex]

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