Question

the algebraic form of an arithmetic sequence is 4n+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 by4​

Answer 1

Answer:

jkakskkoaiksjskakamdjalskjdwi

Answer 2

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,

$\\=> a_{n} = 4n+1$

and n = 1,2,3...

Now,

$\\\\=> a_{1} = 4(1) +1 \\\\ = 4+1 \\\\\\=> a_1 = 5$

If n = 2,

$\\=> a_2 = 4(2)+1 \\\\ => 8+1 \\\\=> a_2 = 9\\\\\\\\If \: \: n=3 ,\\\\\\=> a_3 = 4(3)+1 \\\\\\=> a_3 = 13.$

The sequence is 5 ,9,13..

Hence, the first term is 5.

_______________________

Common difference :

=> d = $a_2  - a_1$

=>  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 .

__________________________

HOPE IT HELPS :)