Question

.The algebraic form of an arithmetic sequence is "4n + 3"

i) Write the common difference
ii) Write the remainder when terms of this sequence are divided by common difference.

iii) Can the 82 be a term of this sequence? Justify.

can you. answer fast​

Answer 1

Step-by-step explanation:

Given :-

The algebraic form of an arithmetic sequence is "4n + 3"

To find :-

i) Write the common difference ?

ii) Write the remainder when terms of this sequence are divided by common difference?

iii) Can the 82 be a term of this sequence? Justify.

Solution :-

Given that

The algebraic form of an arithmetic sequence = "4n + 3"

Let an = 4n + 3 ------------(1)

Put n = 1 then (1) becomes

=> a1 = 4(1)+3

=> a1 = 4 + 3

=> a1 = 7

First term of the AP = 7

Put n = 2 then (1) becomes

=> a2 = 4(2)+3

=> a2 = 8+3

=> a2 = 11

Second term = 11

Common difference = a2-a1

=> d = 11-7

=> d = 4

Common difference of the AP = 4

Now,

The remainder when the first term is divided by the common difference

=> 7/4

=> 1 3/4

The remainder = 3

The remainder when the second term is divided by the common difference

=> 11/4

=> 2 3/4

The remainder = 3

The remainder when the terms are divided by the common difference is 3

The first term = 7

Common difference = 4

Let an = 82

We know that

The nth term of an AP (an) = a+(n-1)d

=> a+(n-1)d = 82

=> 7+(n-1)(4) = 82

=> 7+4n-4 = 82

=> 4n + 3 = 82

=> 4n = 82-3

=> 4n = 79

=> n = 79/4

=> n is a fraction

But n cannot be a fraction . It must be a natural number.

So, 82 is not in the given AP.

Answer :-

i)The Common difference of the AP = 4

ii) The remainder when the terms are divided by the common difference = 3

iii) 82 is not in the given AP.

Used formulae:-

→ The nth term of an AP (an) = a+(n-1)d

• a = First term
• d = Common difference
• n = number of terms
• an = nth term or General term of an AP.