Question

ANSWER ASAP! In an arithmetic sequence, a17 = -40 and

a28 = -73. Explain how to use this information to write a recursive formula for this sequence.

Answer 1

The difference between the given terms is

–73 – (–40) = –33.

The difference between the term numbers is 28 – 17 = 11.

Dividing –33 / 11 = –3.

The common difference is –3.

The recursive formula is the previous term minus 3, or an = an – 1 - 3 where a17 = -40.

Explanation:

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Answer 2

The Recursive Formula of sequence is: 8, 5, 2, -1, -4,...

Explanation:

Arithmetic Sequence is a sequence in which every two neighbor digits have equal distances.

For finding the nth term, we use formula

aₙ = a + (n - 1) d

where, aₙ = value of nth term

a = First term

n = number of term

d = difference

We have given that,

a₁₇ = -40 ⇒ a₁₇ = a + (17 - 1)d

⇒ -40 = a + 16d → (1)

Also, a₂₈ = -73 ⇒ a₂₈ = a + (28 - 1)d

⇒ -73 = a + 27d → (2)

Solving, equation (1) and (2), We get

a = 8, d = -3

Hence, First term = a = 8

Second term = a + d = 8 - 3 = 5

Third term = 5 + d = 2

Fourth term = 2 + d = -1

Thus, The Arithmetic Sequence is: 8, 5, 2, -1, -4,...