Question

Find9term fromthe end towards the first term of ap 5,9,13,......185

Answer 1

$\bold{ \underline{AP : \: \: \: \: 5 , 9 , 13 , . . . . . . . . . . . . 185}}$


$\bold{ \: Common \: \: Difference = 13 - 9 = 9 - 5 = 4}$






$\bold{ \underline{W e \: know, \: \: a_{n} = a + d( n - 1 ) }}$

Hence,


$\bold{185 = 5 + 4(n - 1)} \\ \\ \bold{ 180 = 4(n - 1)} \\ \\ \bold{45 = n - 1} \\ \\ \bold{ \: 46 = n}$






$\bold{ \: hence \: there \: are \: 46 \: terms}$

$\bold{ \underline{And \: \: 9th \: \: term \: \: from \: \: last = ( 46 - 9 )th \: \: term =>37th \: \: term}}$





$\bold{n \: th \: \: ter m \: = a + d(n - 1)} \\ \\ \\ = > \bold{ \: 37th \: term \: = 5 + 4(37 - 1) }\\ \\ \\ = > \bold{37th \: \: term \: = 5 + 144 }\\ \\ \\ \bold{ \underline{\: = > 37 \: th \: \: \: term \: = 149}}$