Question

Write the rule for the nth term of an arithmetic sequence in which a10=46 and d=3

Answer 1

The rule for the nth term of the arithmetic sequence is given by the formula a_n = 19 + (n - 1)×3, where a1 is the first term of the sequence and d is the common difference.

Step-by-step explanation:

To write the rule for the nth term of an arithmetic sequence where the 10th term a10 is 46 and the common difference d is 3, we use the formula:

an = a1 + (n - 1)d

We have that:

a10 is the 10th term of the sequence which is 46.

The common difference d is 3.

Firstly, we need to find a1, the first term of the sequence. We can use the given a10 to find a1.

a10 = a1 + (10 - 1)×3

46 = a1 + 9×3

46 = a1 + 27

a1 = 46 - 27

a1 = 19

Now we can write the rule for the nth term:

an = 19 + (n - 1)×3

This formula allows us to calculate any term in the sequence by substituting the desired term number for n.

Answer 2

Equation for arithmetic sequence
a{n} = a{1} + d(n - 1)

Plug in known values
2 = a{1} + -4(10 - 1)
2 = a{1} - 36
38 = a{1}
a{1} = 38


Plug d = -4 and a{1} = 38 into
arithmetic sequence equation
a{n} = 38 - 4(n - 1)