If the general term of an $A P$ is $2 n - 3$ , find the $A P$ . Also find the sum

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Solution

Genral term of AP is $T_{n} = 2 n - 3$
$T_{1} = 2 - 3 = - 1$
$T_{2} = 2 \times 2 - 3 = 1$
$T_{3} = 2 \times 3 - 3 = 3$
$T_{4} = 2 \times 4 - 3 = 5$
AP is $- 1, 1, 3, 5$
$s_{n} = \frac{n}{2} [2 a + (n - 1) d]$
$s_{n} = \frac{n}{2} [- 2 + (n - 1) 2]$
$s_{n} = n [- 1 + (n - 1)]$
$= n (n - 2)$
$s u m = n^{2} - 2 n$

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