Question

Find the 8th term from end of the A.P. 7, 10, 13, ..., 184.

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{8th\:term\:from\:the\:end=163}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies A.P= 7,10,13,.....,184 \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies 8th \: term\:from\:the\:end= ?$

• According to given question :

$\circ \: \tt{First\:term\:from\:end=184} \\\\ \tt\circ\:Common\:difference=-3\\\\ \tt\circ\:Last\:term=7\\\\ \tt\circ\:n=8$

$\bold{As \: we \: know \: that} \\ \tt: \implies a_{n} = a +( n - 1)d \\ \\ \tt: \implies a_{8}= 184 + (8 - 1) \times ( - 3) \\ \\ \tt: \implies a_{8} = 184 +7 \times ( - 3) \\ \\ \tt: \implies a_{8} =184 - 21 \\ \\ \green{\tt: \implies a_{8} =163} \\ \\ \green{\tt \therefore 163 \: is \: the \: 8th \: term \: from \: the \: end}$

Answer 2

Answer:

$hey$

first term is 7 say "a"

and last term is 184 say "an"

if the no. of terms are n

D ( common difference) = 13-10 = 10-7 => 3

Now we have to find the 8th last term so it will be easier for us if we will reverse the AP

=> 184,181, ..........13,1 0,7

now D = -3 and a = 184

an = 7

Now we have to find 8th term :-

use an = a+(n-1)d

just plug in the values....

a8 = 184 + (8-1)×-3

a8 = 184 -21

a8 = 163