[tex]\large \bold {SOLUTION}[/tex]
[tex]\small\textsf{We have to find first the common difference}[/tex]
[tex]\small\textsf{Use the arithmetic sequence formula} \\ \\ \sf\blue{a_{n} = a_{1}(n - 1)d}[/tex]
[tex]\small\sf\red{a_{n} \: is \: the \: nth \: term \: of \: the \: sequence}[/tex]
[tex]\small\sf\red{a_{1} \: is \: the \: 1st \: term \: of \: the \: sequence}[/tex]
[tex]\small\textsf\red{d is the common difference of the sequence}[/tex]
[tex]\small\textsf\red{n is the position of a number in the sequence}[/tex]
[tex]\small\sf{Let \: a_{n} = 66, \: a_{1} = 10 \: and \: n = 9}[/tex]
[tex]\small\sf{a_{n} = a_{1} + (n - 1)d}[/tex]
[tex]\small\sf{66 = 10 + (9 - 1)d}[/tex]
[tex]\small\sf{66 = 10 + (8)d}[/tex]
[tex]\small\sf{66 + (- 10) = 10 + 8d + ( - 10)}[/tex]
[tex]\small\sf{56 = 8d}[/tex]
[tex]\small\sf{ \dfrac{\cancel{8}d}{\cancel{8}} = \dfrac{56}{8} }[/tex]
[tex]\small\boxed{\green{\sf{d = 7}}}[/tex]
[tex]\small\textsf{Find the 26th term of the sequence. Let d = 7}[/tex]
[tex]\small\sf{a_{n} = a_{1}(n - 1)d}[/tex]
[tex]\small\sf{a_{26} = 10 + (26 - 1)7}[/tex]
[tex]\small\sf{a_{26} = 10 + (25)7}[/tex]
[tex]\small\sf{a_{26} = 10 + 175}[/tex]
[tex]\small\boxed{\green{\sf{a_{26} = 185 }}}[/tex]
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