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Microsoft Word - c9hw.pdf 1. Write the first three terms of the sequence. 3. The formula for the nth term an of a sequence {an } is given below. Find the values of a1 , a2 , a3, and a4. 4. The first term of a sequence along with a recursion formula for the remaining terms is given below. Write out the first ten terms of the sequence. a = n 4 n 4 n + 2 ( Type an integer or a simplified fraction.) a 1 = ( Type an integer or a simplified fraction.) a 2 = ( Type an integer or a simplified fraction.) a 3 = Type ( an integer or a simplified fraction.) a 4 = 2. a = n n + 4 The first three terms are , , and . a 1 = a 2 = a 3 = ( Simplify your answers. Type integers or fractions.) A formula is given below for the term of a sequence . Find the values of , , , and . n t h a n a n a 1 a 2 a 3 a 4 n + 1 a n = ( Type an integer or a fraction.) a 1 = Type ( an integer or a fraction.) a 2 = ( Type an integer or a fraction.) a 3 = ( Type an integer or a fraction.) a 4 = 5. The first term of a sequence along with a recursion formula for the remaining terms is given below. Write out the first ten terms of the sequence. 6. The first term of a sequence along with a recursion formula for the remaining terms is given below. Write out the first ten terms of the sequence. a 1 , a n / (1 n ) = 8 a n + 1 = + 2 a 1 = a 2 Simplify ( your answer.) = a 3 Simplify ( your answer.) = a 4 ( Simplify your answer.) = a 5 ( Simplify your answer.) = a 6 ( Simplify your answer.) = a 7 Simplify ( your answer.) = a 8 ( Simplify your answer.) = a 9 ( Simplify your answer.) = a 10 Simplify ( your answer.) = a 1 , ( 1) a n / = 1 0 a n + 1 = − n + 1 5 a 1 = a 2 Simplify ( your answer.) = a 3 ( Simplify your answer.) = a 4 ( Simplify your answer.) = a 5 ( Simplify your answer.) = a 6 ( Simplify your answer.) = a 7 ( Simplify your answer.) = a 8 ( Simplify your answer.) = a 9 ( Simplify your answer.) = a 10 Simplify ( your answer.) = . 8. Find a formula for the nth term of the sequence. − 2, 1, 6, 13, 22, ... Determine the sequence's formula in terms of n. an = , n ≥ 1 9. Find a formula for the nth term of the sequence where an is calculated directly from the value of n. 2 , 6 , 10 , 14, 18, ... 10. Find a formula for the nth term of the sequence where an is calculated directly from n. . 11. Determine if the sequence {an } converges or diverges. Find the limit if the sequence converges. n an = 3 + (0.3) 7. a = 2 , a = 1 n + 1 n a n n + 3 a = 1 Simplify ( your answer.) a = 2 ( Simplify your answer.) a = 3 ( Simplify your answer.) a = 4 ( Simplify your answer.) a = 5 ( Simplify your answer.) a = 6 ( Simplify your answer.) a = 7 ( Simplify your answer.) a = 8 ( Simplify your answer.) a = 9 ( Simplify your answer.) a = 1 0 Find a formula for the nth term of the sequence in terms of n. for a n = n ≥ 1 , a n = n ≥ 1 for a n = n ≥ 1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 12. Determine whether the following sequence converges or diverges. If it converges, find its limit. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. an = n + 5 14. The formula for the nth term an of a sequence {an } is given below. Find the values of a1 , a2 , a3, and a4. 15. The first term of a sequence along with a recursion formula for the remaining terms is given below. Write out the first ten terms of the sequence. A. The sequence converges, and . ( Simplify your answer.) a l i m n n = B. The sequence diverges. { } a n = 8 n + ( − 1 ) n 8 n 13. A. The sequence converges to . ( Simplify your answer.) a = l i m n n B. The sequence diverges. Write the first three terms of the sequence. The first three terms are , , and . a 1 = a 2 = a 3 = ( Simplify your answers. Type integers or fractions.) a = n 3 n 3 n + 3 ( Type an integer or a simplified fraction.) a 1 = ( Type an integer or a simplified fraction.) a 2 = ( Type an integer or a simplified fraction.) a 3 = Type ( an integer or a simplified fraction.) a 4 = 16. Find the first 4 terms and the eighth term of the recursively defined sequence. c1 = 7, c2 = − 3 , and ck + 2 = ck + ck + 1 , for k ≥ 1 The first term is (Simplify your answer.) The second term is . (Simplify your answer.) The third term is . (Simplify your answer.) The fourth term is . (Simplify your answer.) . 17. Find a formula for the nth term of the sequence in terms of n. . 18. Find a formula for the nth term of the sequence where an is calculated directly from n. a 1 , ( 1) a n / = 8 a n + 1 = − n − 1 2 a 1 = a 2 Simplify ( your answer.) = a 3 ( Simplify your answer.) = a 4 ( Simplify your answer.) = a 5 ( Simplify your answer.) = a 6 ( Simplify your answer.) = a 7 ( Simplify your answer.) = a 8 ( Simplify your answer.) = a 9 Simplify ( your answer.) = a 10 Simplify ( your answer.) = . The eighth term is ( Simplify your answer.) for a n = n ≥ 1 . 19. Determine if the sequence {an } converges or diverges. Find the limit if the sequence converges. Select the correct choice below and fill in any answer boxes within your choice. 20. Does the sequence {an } converge or diverge? Find the limit if the sequence is convergent. Select the correct choice below and, if necessary, fill in the answer box to complete the choice. 21. Does the sequence {an } converge or diverge? Find the limit if