Exam 7: Sequences, Series, and Limits

Find two numbers between 5 and 40 such that they form a geometric sequence with 5 and 40.

Write the series explicitly and evaluate the sum. Use log rules to simply your answer.

Find the eighth term of an arithmetic sequence whose third term is 7 and whose fifth term is 13.

Evaluate the geometric series. Leave the answer in terms of unsimplified powers of the common ratio.

Find the nth term of a recursive sequence given by a₁ = 5, a_{n + 1} = a_n + 4 for n $\ge$ 1.

Find the sum of all three digit even positive integers.

is correct?

Evaluate the arithmetic series. 93 + 94 + 95 + ... + 306 + 307

Give the first four terms of the sequence a_n = 2 + 2ⁿ.

Find the sum of all three-digit positive integers whose last digit equals 3.

Evaluate the geometric series. Leave the answer in terms of unsimplified powers of the common ratio. 5 + 10 + 20 + ... +

Evaluate .

Evaluate .

Evaluate .

Give the first four terms of the sequence . Give the exact answers.

Write the series using summation notation (starting with m = 1).

Evaluate the arithmetic series.

Evaluate . Give the exact answer.

Write the series explicitly and evaluate the sum. Give the exact answer.

Express as a fraction.