Question

NO LINKS!!!!

Margot was doing her homework when her dog bit off a piece of the paper. All she had left was the start of the sequence: 4, 12, ... and the fact that 972 was some term of the sequence.

a. Could the sequence be arithmetic? If so, what is the equation of the nth term and what term number is 972?

b. Could the sequence be geometric? If so, what is the equation of the nth term and what term number is 972?

Answer 1

9514 1404 393

Answer:

a. yes. term 122

b. yes. term 6

Explanation:

a. The first term is 4 and the difference is 12-4 = 8. If 972 is a term of the sequence, there will be an integer value n such that ...

t(n) = t(1) +d(n -1) . . . . . for t(1) = 4 and d = 8

972 = 4 +8(n -1)

968 = 8(n -1)

121 = n -1

122 = n . . . . . . . . the sequence could be arithmetic, with term 122 = 972.

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b. The first term is 4 and the common ratio is 12/4 = 3. If 972 is a term of the sequence, there will be an integer value n such that ...

t(n) = t(1)·r^(n-1) . . . . . for t(1) = 4 and r = 3

972 = 4·3^(n-1)

243 = 3^(n-1)

3^5 = 3^(n -1) . . . . . write 243 as a power of 3

5 = n -1 . . . . . . . . . . equate exponents

6 = n . . . . . . . . . the sequence could be geometric, with term 6 = 972.