Question

In an A.P the 3rd is 20 and 8th term is 50. Find the first term and common difference.​

Answer 1

Step-by-step explanation:

a+2d= 20.....

a+7d = 50......

by elimination method.....

2d -7d = 20-50

-5d = -30

d= 6

a+2d= 20

a+2(6)=20

a=8

1st term= a+d= 8+6 = 14

Answer 2

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

${\bold{\therefore First\:term=8}}$

${\bold{\therefore Common\:difference=6}}$

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

$\underline \bold{Given : } \\ \implies a_{3} = 20 \\ \\ \implies a_{8} = 50 \\ \\ \underline \bold{To \: Find : } \\ \implies First \: term(a) = ?\\ \\ \implies Common \: difference(d) = ?$

• According to given question :

$\implies a_{3} = 20 \\ \\ \implies a + 2d = 20 - - - - - (1) \\ \\ \implies a_{8} = 50 \\ \\ \implies a + 7d = 50 - - - - - (2) \\ \\ \bold{subtracting \: (1) \: from \: (2) : } \\ \implies a + 7d - (a + 2d )= 50 - 20 \\ \\ \implies a - a + 7d - 2d = 30 \\ \\ \implies 5d = 30 \\ \\ \implies d = \frac{30}{5} \\ \\ \bold{\implies d = 6} \\ \\ \bold{Putting \: value \: of \: d \: in \: (1)} \\ \\ \implies a + 2d = 20 \\ \\ \implies a + 2 \times 6 = 20 \\ \\ \implies a = 20 - 12 \\ \\ \bold { \implies a = 8}$