Question #02853

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Answer 1 · 2017-08-24T15:57:02

$T_{n} = 13 - 2 n$ $T_n = 13 - 2n$

Sequence $11, 9, 7, 5, 3$ $11, 9, 7, 5, 3$

First term $\to a = 11$ $-> a = 11$

Common Difference $\to d = T_{2} - T_{1} or T_{3} - T 2$ $-> d = T_2 - T_1 or T_3 - T2$

$\Rightarrow T_{2} - T_{1} = 9 - 11 = - 2$ $rArr T_2 - T_1 = 9 - 11 = - 2$

$\Rightarrow T_{3} - T 2 = 7 - 9 = - 2$ $rArr T_3 - T2 = 7 - 9 = - 2$

Recall $\to T_{n} = a + (n - 1) d$ $-> T_n = a + (n - 1) d$

$:. T_n = 11 + (n - 1) - 2$

$rArr T_n = 11 + (-2n + 2)$

$rArr T_n = 11 - 2n + 2$

Collect like terms

$rArr T_n = 11 + 2 -2n$

$rArr T_n = 13 - 2n$