Question

The algebraic form of an arithmetic sequence is 5n+3
a)what is the common difference
b)what is its first term

Answer 1

Answer:

We know that if a sequence is given by {an=f(n)}, then the first term of the sequence is determined by putting n = 1 in the formula for the general term of the sequence, i.e. a=f(1).

Now, we have

an=5n+3

Hence, we have

a=5(1)+3=8

Hence the first term of the arithmetic sequence is 8.

Now, we have

an=5n+3 (i)

Also by Euclid’s division lemma, if a,b are any two integers, then there exist unique integers r and q such that a=bq+r,0≤r≤b−1.

Hence, we have

an=5q+r,0≤r≤4 (ii)

Since q and r are unique, from equations (i) and (ii), we get

n = q and r = 3.

Hence the remainder obtained on dividing the term of the sequence by 5 is 3.

Note: Alternative solution for part a:

We have

an=5n+3=5(n−1+1)+3=5+3+5(n−1)

Hence, we have

an=8+5(n−1)

Comparing with the formula for the general term of an arithmetic sequence, i.e. an=a+(n−1)d, we get

a=8,d=5

Hence, the first term of the sequence is 8.

and the common difference is 5

Answer 2

Answer:

n = q and r = 3. Hence the remainder obtained on dividing the term of the sequence by 5 is 3. Hence, the first term of the sequence is 8.

Step-by-step explanation:

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