Question

Answer this question...
No spamming plz..


Find the number of terms in the arithmetic progression 8, -3, -14,..., -289

Answer 1

$\huge\mathfrak{solution}$

Given :

8 , -3,-14........,-289 are in AP

●First term= a = 8

● Common difference = a2-a1

= -3-8=-11

and

●Last term = tn =-289

As we know that

◆ tn = a+ (n-1) d

=> -289= 8+(n-1)-11

=> -289= 8-11n+11

=>-289=19-11n

=>11n= 19+289

=> n = 308/11

=> n =28

Hence, the number of terms is

$\purple{\bold{ \boxed{ \: 28} }}$

Answer 2

Answer:

n = 28

Step-by-step explanation:

Series is 8, -3, -14 .... -289

First term a = 8

Based on the given series, the common difference is,

d = -3 - 8 = -11

Last term = an = -289

Let the number of terms be n. We will therefore be solving for n.

To determine the nth term, use the following formula,

an = a + (n - 1) * d

substitute the values of a, an and d in the above equation.

To solve for n, use the substitution method of system of equations.

=> -289 = 8 + (n - 1) * (-11)

=> -289 = 8 - 11n + 11

=> -289 = 19 - 11n

=> -289 - 19 = -11n

=> -308 = -11n

=> n = 308/11

=> n = 28

The arithmetic series 8,-3,-14,.... -289 will consists of 28 terms.

Hence, the number of terms = 28

Hope it will help you!