Question

A) Use for loop to generate a row vector of an arithmetic series of = 5 ― 2 where = 1.....50.

b) Use for loop to generate a row vector of an arithmetic series of = 0.4 where = 1.....50.
c) Use for loop to generate a row vector of a geometric series of = ( ―1)ⁿ(3/4)ⁿ
d) Use for loop to generate a row vector of a geometric series of = (0.98) where = 1.....50.

Answer 1

To generate the row vectors, you can use for loops in programming languages like Python. For arithmetic series with common differences of 5-2 and 0.4, the for loops would involve simple equations. For geometric series, the for loops would involve using the exponentiation operator and a multiplier.

Step-by-step explanation:

To generate a row vector of an arithmetic series for part (a), starting from 1 and ending at 50, with a common difference of 5-2, you can use a for loop in a programming language like Python. Here is an example:

vector = []
for i in range(1, 51):
value = 1 + (5-2) * (i-1)
vector.append(value)
print(vector)

For part (b), using a common difference of 0.4, the code would look like this:

vector = []
for i in range(1, 51):
value = (i-1) * 0.4
vector.append(value)
print(vector)

For parts (c) and (d), which involve geometric series, we can also use a for loop to generate the row vectors. Here is an example for part (c):

vector = []
for i in range(1, 51):
value = (-1) ** i * (3/4) ** i
vector.append(value)
print(vector)

And here is an example for part (d):

vector = []
for i in range(1, 51):
value = 0.98 ** (i-1)
vector.append(value)
print(vector)