In the A.P. $12, 19, 26$ , ...... find $T_{n}$ and hence find $T_{15}$

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Solution

Given that: $a = 12, d = 19 - 12 = 7, T_{n} = ?, T_{15} = ?$
$T_{n} = a + (n - 1) d$
$T_{n} = 12 + (n - 1) 7 = 12 + 7 n - 7$
$T_{n} = 5 + 7 n$
$∴ T_{15} = 5 + 7 (15) = 5 + 105$
$T_{15} = 110$

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