Question

What is the difference between an arithmetic and geometric sequence?

Answer 1

Arithmetic formula: \[ t_n = t_1 + (n - 1)d \]
\[t_n \] is the nth term, \[t_1 \] is the first term, and d is the common difference

Answer 2

Geometric formula: \[ t_n = t_1 . r^(n - 1) \]
\[t_n \] is the nth term, \[t_1 \] is the first term, and r is the common ratio.

Answer 3

Did you get the concept @kenneyfamily

Answer 4

yes!

Answer 5

Arithmetic sequences have a constant difference between terms:

1, 3, 5, 7,... The difference between successive terms is 2.

The general formula for the nth term is a(n) = a(1) + d·(n-1) where a(1) = the initial term
, d = difference between terms.

So to find the 5th term (which we can see in the sequence should be 9), we plug in n = 5

a(5) = 1 + 2·(5-1) = 1+2·4 = 9

WHEREAS
Geometric sequences have a constant ratio between terms:
2, 6, 18, 54, ... The ratio between successive terms is 3.

The general formula for the nth term is a(n) = a(1)·r^(n-1), where a(1) is the first term and r is the ratio.

So to find the 5th term (which we can see in the sequence should be 162), we plug in n = 5
EXAMPLE..
a(5) = 2·3^(5-1) = 2·3^4 = 2·81 = 162

Answer 6

arithmetic sequence is a sequence of numbers such tht the difference of two condegutive numbers is a constant
geometirc sequence is a sequence of numbers such tht the quotient between two consegutive numbers is a constant