Question

Consider the sequence 60, 53, 46, 39, 32, 25, ...The common difference of this sequence isSelect oneformula for the sequence isThe tenth term for this sequence isSelect one

Answer 1

We have here an arithmetic progression.

We have that the common difference is:

53- 60 = - 7

46 - 53 = - 7

39 - 46 = - 7

And so on.

Therefore, the common difference of this sequence is d = -7. The progression is decreasing.

We can find the formula for the sequence using the general formula for arithmetic progressions:

`a+(n-1)d`

Where

a is the first term of the arithmetic progression.

n is the n term of the sequence.

d is the common difference ( d = -7 in this case).

Then, we have that the formula for this sequence is:

`60+(n-1)(-7)=60-7(n-1)=67-7n`

We can check that the second, and six terms are:

`60-7(2-1)=60-7=53,60-7(6-1)=60-7(5)=60-35=25`

We have:

60 (1), 53 (2), 46 (3), 39 (4), 32 (5), 25 (6), ...

Therefore, the tenth term for this sequence is:

`60-7(10-1)=60-7(9)=60-63=-3`

Hence, the tenth term is -3.