Question

Given the first three terms of the arithmetic sequence

Answer 1

The value of p in the arithmetic sequence is -1.

Arithmetic progression

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

The common difference (d) is:

d = (p + 5) - (2p + 5) and d = (2p + 7) - (p + 5)

(p + 5) - (2p + 5) = (2p + 7) - (p + 5)

-p = p + 2

p = -1

The value of p in the arithmetic sequence is -1.

Find out more on Arithmetic progression at: brainly.com/question/6561461

Answer 2

The value of p in the sequence is 3

Description of arithmetic sequence

Arithmetic sequence is a type of sequence which have a common difference between each term in the sequence.

Data obtained from the question

•First term (T₁) = 2p – 3

•2nd term (T₂) = p + 5

•3rd term (T₃) = 2p + 7

•Value of p =?

How to determine the value of p

Common difference = T₂ – T₁ = T₃ – T₂

Using the above, the value of p can be obtained as follow:

T₂ – T₁ = T₃ – T₂

(p + 5) – (2p – 3) = (2p + 7) – (p + 5)

Clear brackets

p + 5 – 2p + 3 = 2p + 7 – p – 5

Collect like terms

p – 2p – 2p + p = 7 – 5 – 5 – 3

–2p = –6

Divide both side by –2

p = –6 / –2

p = 3

Therefore, the value of p is 3

Learn more about arithmetic sequence:

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