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ANSWER

The fiftieth term is 286.

EXPLANATION

A sequence with a common difference,

[tex]d = 6[/tex]

is an arithmetic progression.

The nth term is

[tex]a_n=a_1 + d(n - 1)[/tex]

If the sixth term is 22 then,

[tex]22=a_1 + 6(6 - 1)[/tex]

[tex]22=a_1 + 30[/tex]

[tex]22 - 30=a_1[/tex]

[tex]a_1 = - 8[/tex]

The fiftieth term is

[tex]a_{50}= - 8 + 6(50 - 1)[/tex]

[tex]a_{50}= - 8 + 6 \times4 9[/tex]

[tex]a_{50}=- 8 +294[/tex]


[tex]a_{50}=286[/tex]

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