Answer each questions correctly. Remember, you are only required to show ALL of your work for questions 1, 2, 3, 4, and 5. After that, you can only put the answers if you want to (NO WORK REQUIRE FOR THE REST OF THE QUESTIONS).

Math 130 - Homework 9 Due 12/8/2022 Name: 1. Find the sum by formula n(a1 + an) 100 of C(-1) k 2 K = 1 2. Find the sum of the following geometric series: 15, ,, ' 8, ...} 5 5 5 3. Express the following repeating decimal as a fraction: .7777777... 4. The second and fifth term of a geometric sequence are 10 and 1250 respectively. Is 31, 250 a term in this sequence? If so, which term is it? 5. Consider the following sequence { 14: 16' 64' 256' . . .}. Determine whether or not the sequence is Geometric and if so, find r. Then write the formula for the nth term.Find the common ratio for the geometric sequence that starts at a1. -4, - 1, 1 16 64 . . 4 r = PreviewDetermine whether the sequence is geometric. If so, nd the common ratio. { 6, 12, 24, 48, 96, ...} Determine whether the sequence is geometric. If so, nd the common ratio. 1 1 4, 2, 1,, ,... 2 4 No Determine whether the sequence is geometric. If so, find the common ratio. {0.4, - 2, 10, - 50, 250, ...} O Yes, r = ONoWrite the first five terms of the geometric sequence, given the first term and the common ratio. Answer exactly. a1 = 16 , r = 16,Write the rst four terms of the geometric sequence (starting at (11), given these two terms. as = 243 , (1.11 = 6561 Find the specified term for the geometric sequence, given the first term and common ratio. The first term is 4, and the common ratio is 5. Find the 4th term. a4 =Find the specified term for the geometric sequence, given the first term and common ratio. The first term is 16, and the common ratio is . Find the 4th term. a4 PreviewFind the specified term for the geometric sequence, given the first four terms. {1, - 2, 4, - 8, ...} ag\fFind the specified term for the geometric sequence given. a1 = - 6, an = - 4an -1, find ag. ag PreviewFind the specified term for the geometric sequence given. {3, 9, 27, 81, ..., 6561} n = PreviewUse the formula for the sum of the first n terms of each arithmetic sequence. 27 + 33 + 39 + ... + 87 =Use the formula for the sum of the first n terms of the geometric sequence to find the indicated sum. 9 6. 40-1 n=1Determine whether the innite series has a sum. If so, nd the sum. If not, state the reason. 2 + 0.8 + 0.32 + 0.128 + 0.0512 + The sum does not exist because the series is not geometric The series is geometric, but 1' > 1, so the sum does not exist. Use the formula for the sum of the first n terms of an arithmetic series to find the sum. 0.4 + 1.8 + 3.2 + 4.6 + 6 + 7.4 =Use the formula for the sum of the first n terms of a geometric series to find the sum. So for the series 4 + 12 + 36 + 108 + ... S6 =