Question

Determine whether each sequence is arithmetic. If so, identify the common difference and find the 32 nd term of the sequence. 7,10,13,16, . . . . .

Answer 1

Common difference = 3 , 32nd term = 100

The arithmetic sequence is the sequence where the common difference remains constant between any two successive terms.

The given series is

7, 10, 13, 16....

common difference = 10-7 = 13- 10= 16-13 = 3

Therefore there is a common difference between the two consecutive number.

In this series the common difference is 3.

Hence we get to know that the given series is an arithmetic series.

To identify the 32nd term we have a formula:

$t_{n}$ = a +(n-1)d

Here a = first number of the series

        n = number of series

        d = common difference

$t_{32}$ = 7 + (32-1)3

    = 7 + 31×3

    = 7 + 93

    = 100

Hence the 32nd term is 100.

To know more about the arithmetic series refer to the link given below:

brainly.com/question/22972770

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