Question

If the first term of an A.P.is -18 and its 10th term is zero then find its common difference

Answer 1

Step-by-step explanation:

A = first term =-18

a10= a+9d

0=-18+9d

therefore,

9d= 18

d = common difference= 2

Answer 2

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

${\bold{\therefore Common\:difference=2}}$

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

• In the given question information given about the first term of an A.P.is -18 and its 10th term is zero.

• We have to find its common difference.

$\underline \bold{Given : } \\ \implies a = - 18 \\ \\ \implies a_{10} = 0 \\ \\ \underline \bold{To \: Find : } \\ \implies Common \: difference = ?$

• According to given question :

$\bold{Formula \: of \: n_{th} \: term : } \\ \implies a_{n} = a + (n - 1)d \\ \\ \implies a_{10} = a + (10 - 1)d \\ \\ \bold{putting \: given \: values : } \\ \implies 0 = - 18 + 9d \\ \\ \implies 9d = 18 \\ \\ \implies d = \frac{ \cancel{18}}{ \cancel{9}} \\ \\ \bold{\implies d = 2} \\ \\ \bold{Alternate \: method : } \\ \\ \implies a_{10} = a + 9d \\ \\ \implies 0 = - 18 + 9d \\ \\ \implies 9d = 18 \\ \\ \implies d = \frac{ \cancel{18}}{ \cancel9} \\ \\ \bold{\implies d = 2} \\ \\ \bold{\therefore Common \: difference \: of \: this \: A.P \: is \: 2}$