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Barbara received a chain text that she forwarded to five of her friends. Each of her friends forwarded the text to five more friends, and so on.

a. Find the first five terms of the sequence representing the number of people who receive the text in the nth round.
b. Write a recursive formula for the sequence.
c. If Barbara represents \(a_1\), find \(a_5\).

A)
a. 5, 25, 125, 625, 3125
b. \(a_n = 5a_{n-1}\)
c. 3125

B)
a. 1, 5, 25, 125, 625
b. \(a_n = 5a_{n-1}\)
c. 625

C)
a. 1, 5, 25, 125, 625
b. \(a_n = 5a_{n-1}\)
c. 3125

D)
a. 5, 10, 15, 20, 25
b. \(a_n = 5a_{n-1}\)
c. 25

Answer :

Final answer:

The question refers to a mathematical sequence where each person forwards a text to five others. The first five terms of this sequence are 1, 5, 25, 125, 625. The recursive formula is represented as aₙ = 5aₙ₋₁, and the fifth term (assuming Barbara is the first term) is 625.

Explanation:

The question revolves around sequences and series, which is a part of mathematics. Here we're trying to find out how many people will receive a chain text in each round if each person forwards it to five others.

a) The first five terms of the sequence, which represent the number of people who receive the text in each round, are 1 (Barbara), 5, 25, 125, 625. These numbers are generated by multiplying the previous term by 5, which is the number of new people each person forwards the text message to.

b) The recursive formula for this sequence can be expressed as aₙ = 5aₙ₋₁. This formula describes the relationship between each term and the previous term in the sequence.

c) If Barbara represents a₁ (the first term in the sequence), then the fifth term, a₅, is 625. This means, in the fifth round, the text message is received by 625 people.

Learn more about Sequences and Series here:

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