Question

Find the nth term of the Arithmetic Progression:-10,-15,-20,.......?​

Answer 1

Step-by-step explanation:

-10 , -15 , -20 ,......

In above Arithmetic progression ,

a = -10 , d = -15 + 10 = -5

nth term An = a + (n-1)d

= -10 + (n-1)(-5)

= -10 - 5n + 5

= -5n - 5 = -5(n + 1)

Answer 2

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

$\green{\tt{\therefore{nth\:term=-5n-5}}}$

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

$\green{\underline \bold{Given :}} \\ \tt: \implies Arithmethic \: progression(A.P)= - 10,- 15,- 20,.... \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies nth \: term = ?$

• According to given question :

$\tt \circ \: First \: term = - 10 \\ \\ \tt \circ \: Common \: difference = - 15 - ( - 10) = - 5 \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies a_{n} = a + (n - 1)d \\ \\ \tt: \implies a_{n} = - 10 + (n - 1) \times - 5 \\ \\ \tt: \implies a_{n} = - 10 + ( - 5n + 5) \\ \\ \tt: \implies a_{n} = - 10 - 5n + 5 \\ \\ \green{\tt: \implies a_{n} = - 5n - 5} \\ \\ \green{\tt \therefore nth \: term \: is \: - 5n - 5}$