Question

Find the 75th term: 88, 81, 74, 67, 60

Answer 1

Answer:

-430

Step-by-step explanation:

this is an arithmetic sequence, meaning that it decreases by the same number each time.

in this case, the sequence goes down by seven each time.

i can tell this because to go to from 88 to 81, you have to subtract seven and to go from 81 to 74, you have to subtract seven, and so on..

in other terms: -7n

we then have to subtract -7 from 88 to form our formula

88--7=95

therefore, our formula is -7n+95

now we have to find the 75th term.

to do this, all we have to do is subsitute 75:

-7n+95

-7(75)+95

-525+95

leaving us with an answer of: -430

Answer 2

Answer:

a₇₅ = - 430

Step-by-step explanation:

There is a common difference between consecutive terms, that is

d = 81 - 88 = 74 - 81 = 67 - 74 = 60 - 67 = - 7

This indicates the sequence is arithmetic with nth term

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 88 and d = - 7 , then

a₇₅ = 88 + ( 74 × - 7) = 88 - 518 = - 430