Question

find the nth term...​

Answer 1

hey Mate ....

☆SOLUTION -

8 , 5 , 2 , -1 , -4 , -7

a1 = 8 , a2 = 5

d = a2 - a1

= 5 - 8

= -3

a = 8 , d = -3 , An = -7

By Using the formula -

An = a + ( n -1 ) d

-7 = 8 + (n -1 ) ( -3)

-7 -8 = ( n -1 ) (-3)

-15 = ( n -1 ) ( -3)

-15 / -3 = n -1

5 = n - 1

5 +1 = n

6 = n

☆ n = 6 ☆

▪ So , the number of terms ( nth ) term is 6 ▪

Answer 2

Answer:

$\boxed{\underline{\Huge{\texttt{6}}}}$

Step-by-step explanation:

$\texttt{AP = 8, 5, 2, -1, -4, -7}\\\texttt{Here,}\\a_1 = 8,\: a_2 = 5, \\d = a_2-a_1 = 5-8 = \bold{-3},\\a_n = -7\\\texttt{Using the AP formula;}\\a_n = a_1 + ( n -1 ) d\\\implies -7 = 8 + (n -1 ) ( -3)\\ \implies -7 -8 = ( n -1 ) (-3) \\\implies -15 = ( n -1 ) ( -3) \\\\\implies \dfrac{-15}{-3} = n -1 \\\\\implies 5 = n - 1\\\implies 5 +1 = n\\\implies 6 = n \\\\\therefore \texttt{The n}^\texttt{th}\texttt{ term is = 6}$