Question

508. In an arithmetic progression, if
17 is the 3rd term, -25 is the 17th
term, then -1 is which term?
एक समांतर श्रेणी में, यदि 17 तीसरा पद है,
-25 17 वां पद है, तो -1 कौन सा पंद है?
(a) 10 (b) 11 (c)9 (d) 12​

Answer 1

Answer:

see the image for answer

Answer 2

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

${\bold{\therefore n=9}}$

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

$\underline \bold{Given : } \\ \implies a_{3} = 17 \\ \\ \implies a_{17} = - 25 \\ \\ \implies a _{n} = - 1 \\ \\ \underline \bold{To \: Find : } \\ \implies n = ?$

$\bold{For \: a _{3}}\\ \implies a_{3} = 17 \\ \\ \implies a + 2d = 17 - - - - - (1) \\ \\ \bold{For \: a _{17}}\\ \implies a_{17} = - 25 \\ \\ \implies a + 16d = - 25 - - - - - (2) \\ \\ \bold{Subtracting \: (2) \: from \: (1)} \\ \implies a + 2d - a - 16d = 17 - ( - 25) \\ \\ \implies - 14d = 42 \\ \\ \implies d = \frac{ - 42}{14} \\ \\ \bold{\implies d = - 3} \\ \\ \bold{Putting \: value \: of \: d \: in \: (1)} \\ \implies a + 2d = 7 \\ \\ \implies a + 2 \times - 3 = 7 \\ \\ \implies a - 6 = 7 \\ \\ \implies a = 17 + 6 \\ \\ \bold{ \implies a = 23} \\ \\ \bold{For \: finding \: number \: of \: term } \\ \implies a_{n} = a + (n - 1)d \\ \\ \implies - 1 = 23 + (n - 1) \times - 3 \\ \\ \implies - 1 - 23 = - 3 n+ 3 \\ \\ \implies - 24 - 3 = - 3n\\\\\implies n=\frac{-27}{-3}\\\\\bold{\implies n=9 }$