Question

the algebraic form of an arithmetic sequence is 6n+2 what is the first term and common difference of this sequence​

Answer 1

Answer:

For any arithmetic sequence, first term has n=1. Hence first term is 6+2=8

6n+2

= 6n-6+8

=8+6(n-1).

Comparing with the standard expression of nth term of an arithmetic progression [a+d(n-1)] we have,

a=8, d=6

Step-by-step explanation:

Answer 2

The first term of the sequence is 8 and the common difference is 6.

Step-by-step explanation:

According to the given information, the algebraic form of an arithmetic sequence is 6n+2.

Now, we know that in an arithmetic sequence, when a is the first element of the arithmetic series, b is the last term of the arithmetic series, d is the common difference present between the terms of the series and n is the place value of a particular element and n  represents the nth term of the arithmetic sequence, the formula is

b = a + (n-1)d

Now, since 6n+2 is the algebraic form of the sequence, and represents the nth term of the sequence, putting n = 1, we get,

6(1) +2 = 6+2 = 8, which is the first term of the sequence.

Now, a = 8 here.

Then,

again, putting n = 2, to find the second term of the series, we get,

6(2)+2 = 12 + 2 = 14.

Thus, the common difference d  = 14 - 8 = 6.

Thus, the first term of the sequence is 8 and the common difference is 6.

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