Question

The 20th term from the end of AP 3,8,13,..........253 is

Answer 1

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

$\green{\tt{\therefore{20th\:term\:from\:the\:end=158}}}$

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

$\green{\underline \bold{Given :}} \\ \tt: \implies A.P= 3,8,13,....,253 \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies 20th \: term \: form \: the \: end = ?$

• According to given question :

$\tt \circ \: First \: term = 253 \\ \\ \tt \circ \: Common \: difference = - 5 \\ \\ \tt \circ \: n = 20 \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies a_{n} = a + (n - 1)d \\ \\ \tt: \implies a_{20} = 253 + (20 - 1) \times - 5 \\ \\ \tt: \implies a_{20} =253+ 19 \times - 5 \\ \\ \tt: \implies a_{20} =253- 95 \\ \\ \green{\tt: \implies a_{20} =} \\ \\ \green{\tt \therefore 20th \: term \: from \: the \: end \: is \: 158}$

Answer 2

$\tt{\orange{\huge{Hello!!! }}} B.Q$

QUESTION :

The 20th term from the end of AP 3,8,13,..........253 is

ANSWER :

The 20th term from the end in the above series is 163.

SOLUTION :

$\tt{\red{\leadsto{Given \::- }}} \\ \\</p><p></p><p>Consider \ the \ reverse \ of \ the \ above \ series.$

=> New Seríes :

253 , 248 , .... , 3

a = 258

=> d = 8 - 3 = 5 { New D = -5 as the series is reversed... }

$\tt{\blue{\leadsto{Formulae \: Used \::- }}}$

$\tt{\purple{\mapsto{ a_{n} = a + (n-1) d }}}$

$\tt{\green{\implies{a_{20} = 258 - 19 \times 5 = 258 - 95 = 163}}}..........(A)$