determine the 2nd term and rth …
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Sia ? 6 years, 6 months ago
Given a6 = 12
{tex}\Rightarrow{/tex} a + (6 - 1)d = 12
{tex}\Rightarrow{/tex} a + 5d = 12 ............(i)
and, a8 = 22
{tex}\Rightarrow{/tex} a + (8 - 1)d = 22
{tex}\Rightarrow{/tex} a + 7d = 22 ............(ii)
Subtracting equation (i) from (ii), we get
(a + 7d) - (a + 5d ) = 22 - 12
{tex}\Rightarrow{/tex} a + 7d - a - 5d = 10
{tex}\Rightarrow{/tex}2d - 10
{tex}\Rightarrow \quad d = \frac { 10 } { 2 } = 5{/tex}
Using value of d in equation (i), we get
a + 5 {tex}\times{/tex} 5 = 12
{tex}\Rightarrow{/tex} a = 12 - 25 = -13
nth term(an) = a + (n - 1)a
= -13 + (n - 1)(5)
= 5n - 18
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