Question

the algebraic form of an arithmetic sequence is 3n-1 a)First term? b)what is the remainder on dividing the terms of this sequence by 3.​

Answer 1

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Answer 2

Step-by-step explanation:

Given :-

The algebraic form of an arithmetic sequence is 3n-1

To find :-

Find the following :

a)First term?

b)what is the remainder on dividing the terms of this sequence by 3?

Solution :-

Given that

The algebraic form of an arithmetic sequence = an = 3n-1 --------------(1)

Put n = 1 in (1) then

a1 = 3(1)-1

=> a1 = 3-1

=> a1 = 2

First term = 2

Put n = 2 in (1) then

=> a2 = 3(2)-1

=> a2 = 6-1

=> a2 = 5

Common difference (d) = a2-a1

=> d = 5-2

=> d = 3

The general form of an AP : a ,a+d,a+2d,...

a = 2

a+d = 2+3 = 5

a+2d = 2+2(3) = 2+6 = 8

The AP: 2,5,8,...

If we divide the terms by 3 then the remainder = 2/3 = 0+(2/3)

5/3 = 1+(2/3)

8 /3 = 2+(2/3)

The remainders = 0,1,2,...

Answer :-

a) The first term of the AP = 2

b) The remainders on dividing the terms of this sequence by 3 are 0,1,2,...

Used formulae:-

• The general form of an AP : a ,a+d,a+2d,...