Question

consider the arithmetic sequence 18, 176, 172
a) Is 0 a term of this sequence. Justify?
b)Find the 20th term of the sequence?
c)How many positive terms are there in this sequence? ​

Answer 1

Answer:

180 , 176 , 172.............

let a & d be the first term and and the common difference respectively

a = 180

d = 176 - 180 = -4

a) $t_{n} = 0$

$t_{n} = a + (n - 1)d$

$0 = 180 + (n - 1)(-4)$

$-180 = (n - 1)(-4)$

$\frac{-180}{-4} = (n - 1)$

$n - 1 = 45$

$n = 45 + 1$

$n = 50$

Thus yes 0 is the 50th term of the following AP

b) $t_{20} = a + (n - 1)d$

$t_{20} = 180 + (20 - 1)(-4)$

$t_{20} = 180 + (19)(-4)$

$t_{20} = 180 - 76$

$t_{20} = 104$

c) As we know that the very next term after 0 will be -ve thus there are 50 +ve terms in this AP

Answer 2

Answer:

Step-by-step explanation:

an= a+(n-1)d

0=180+(n-1)-4

0=180+-4n+4

0=184+-4n

0-184=-4n

-184=-4n

n=-184/-4=46

0 is the 46th term of this squence