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2. The algebraic form of an arithmetic sequence is 4 n+1.
a) What is its common difference?
b) What is its first term?
c) What is the remainder when each term of this sequence is divided by 4?

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Answer:

Given:-

The algebraic form of an arithmetic sequence is 4n+1.

To find:-

common difference.

first term

remainder when each term of the sequence is divided by 4.

Solution:-

Given,

and n = 1,2,3...

Now,

If n = 2,

The sequence is 5 ,9,13..

Hence, the first term is 5.

Common difference :

=> d =

=>  9- 5

=> d = 4.

Hence, common difference is 4.

Remainder :

=> 5/4 = 4(4) +1

Here, remainder =1

=> 9/4 = 4(2)+1

Here, remainder =1

=> 13/4 = 4 (3)+1

Here , remainder = 1.

Therefore, the remainder when each term of this sequence is divided by 4 is 1 .

Step-by-step explanation:

Answer:

Below in bold.

Step-by-step explanation:

The nth term = a + d(n - 1)  where a = first term and d = common difference

= dn + a - d

So comparing this to 4n + 1:

a) d = 4

b)  a - d = a - 4 = 1

so a first term = 5.

c) (4n + 1) / 4 = n remainder 1

The remainder is 1.

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