sequences and series

The first term of a geometric sequence is 3. The common ratio is -2. List the first four terms.

The first term of an arithmetic sequence is 2. The common difference is 5. Find the simplified explicit formula for the n^th term. (i.e., u_n = __________)

• 53.07

• 48.6

• 26.07

• 1.8

In a geometric sequence, u₄ = 405 and u₇ = 10935. Find the first term (u₁).

• 3

• 5

• 15

• 45

Evaluate the sum shown here.

• 49

• 98

• 140

• 203

Is it possible to find the sum of all terms of the infinite geometric series with u₁ = 7 and r = -(5/4)?

• yes

• no

Evaluate S_n for the series 34 + 29 + 24 + 19 + ..., for the first 80 terms (i.e., n = 80).

• -18520

• -2325

• -13080

• -26160

• 6

• 7

• 8

• 9

France had about 8700 new cases of Covid-19 on 7.April.2020. If the spread rate of the virus in France under quarantine was consistently 0.85, how many new cases of the virus would there be on 30.April.2020?

• about 176

• about 207

• about 244

Write the explicit formula for the following geometric sequence:

3, -12, 48, -192, ...

• a_n = 4(3)^n-1

• a_n = 3(4)^n-1

• a_n = -4(3)^n-1

• a_n = 3(-4)^n-1