1. Select the answers that best complete the given statements. A sequence in which each term after the first is obtained by multiplying the preceding term by a fixed nonzero constant is called a/an (1) sequence. The amount by which we multiply each time is called the (2) of the sequence. (1) O geometric (2) O constant factor O arithmetic O common ratio O addition term 2. Fill in the blanks so that the resulting statement is true. The nth term of the sequence is given by the formula an = where a, is the and r is the of the sequence. The nth term of the sequence is given by the formula an = (1) - where a, is the (2) and r is the (3) of the sequence. (1) O ar-1 O a, + nr, ) O last term Onth term O agro+ 1 O a1 - (n- 1)r, difference O common difference O common ratio O a, + ( n - 1 )r, O = (2, +r ). O first term O a, - nr, r O 7 (a1 + an) (3) O difference O common difference common ratio O first term nth term O last term3. Select the answers that best complete the given statements. The sum, S , of the first n terms of a geometric sequence is given by the formula S = (1) In the formula for S , a, is the (2) In the formula for S, r is the (3) r# 1. (1) ay (1 -r ) (2) O first term. (3) O last term, O (1 -r) O last term. common difference, a, (1 -17+ 1 ) O second term. O common ratio, O O nth term. O constant factor, (1 - r) an (1 -," ) O (1-r) a, (1 - r) O 1-r4. Select the answers that best complete the given statements. An infinite sum of the form a, tar+ aqr + aqr + ... is called a/an (1) If (2). its sum, S, is defined. If S is defined, it is given by the formula S = (3) The series does not have a sum if (4) (1) O infinite geometric sequence. (2) 0 -1 1. OO finite geometric series. O -1ers1, O O Irls1. O a (1 - r) . O 1 - 1 5. Determine whether the sequence is arithmetic or geometric. 1, -6, 36, - 216, 1296, ... The sequence is (1) (1) O geometric. O arithmetic. 6. Write the first five terms of the geometric sequence. an =4an - 1, 21 =57. Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the following sequence with the given first term, a, , and common ratio, r. Find ayo when a, = 8 and r = 3. 810 (Type an integer or a decimal.)8. Write a formula for the nth term of the following geometric sequence. Then use the formula for a to find as, the 5th term of the sequence. 2, 6, 18, ... Enter a formula for the nth term of the geometric sequence. an Enter the 5th term of the geometric sequence. as (Simplify your answer.) 9. Write a formula for the general term of the geometric sequence. Then use the formula for a,, to find ay, the seventh term of the sequence. 16, 4, 1, . ." (Use integers or fractions for any numbers in the expression.) (Type an integer or a simplified fraction.) 10. Find the sum of the first 12 terms of the geometric sequence shown below. 3, 6, 12, 24, ... The sum of the first 12 terms is 11. Find the sum of the first 13 terms of the geometric sequence shown below. 5, -10, 20, ... The sum of the first 13 terms is . (Round to two decimal places as needed.)12. Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. 9 6-2 i=1 9 6.2= i=1 13. Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. 5 i+ 1 3 101 5 i+ 1 (Type an integer or a simplified fraction.) i=114. Find the sum of the infinite geometric series. 1+ 1 2 8 1 1 1 2 4 (Simplify your answer.) 15. Find the sum of the infinite geometric series. 2+ -. 2 5 The sum of the infinite geometric series is (Type an integer or a simplified fraction.) 16. Find the sum of the infinite geometric series. 6(-0.1)-1 i =1 6(-0.1) -1 = (Round to two decimal places.) 1=1 17. Express the following repeating decimal as a fraction in lowest terms. 7 7 7 7 0.7=. 10 100 1000 10,000 0.7 = (Type an integer or a simplified fraction.)18. Express the repeating decimal as a fraction in lowest terms. 89 89 0.89 = 100 10,000 1,000,000 0.89 = (Type an integer or a simplified fraction.) 19. Express the following repeating decimal as a fraction in lowest terms. 0.367 0.367 = (Type an integer or a simplified fraction.) 20. If zan} and (bry equal the following, find a + be. {an } = - 15, 60, -240, 960, . (on} = 15, -2, - 19, -36, .. ag + be21. Find a, and ag for the following geometric sequence. 250, ap, ag. 2 The value of a, in the given geometric sequence is The value of a, in the given geometric sequence is