Several terms of a sequence {an} n=1 are given below. 1 1 1 1 6'36' 216' 1,296 a. Find the next two terms of the sequence. b. Find a recurrence relation that generates the sequence. c. Find an explicit formula for the general nth term of the sequence. a. Find the next two terms of the sequence. a6 a7 (Simplify your answers.) 00 1 Consider the infinite series k=1 k+2 Evaluate the first four terms of the sequence of partial sums. The first partial sum is S = (Type an integer or a simplified fraction.) Suppose the sequence (an} is defined by the recurrence relation an+1 = 2nan, for n = 1, 2, 3,..., where a = 10. Write out the first five terms of the sequence. Suppose the sequence (an} is defined by the recurrence relation an+1 = 2nan, for n = 1, 2, 3,..., where a = 10. Write out the first five terms of the sequence. 1 Suppose the sequence {a} is defined by the explicit formula a = n+5 for n = 0, 1, 2, 3,.... Write out the first four terms of the sequence. ao (Simplify your answer.) Evaluate the following integral or state that it diverges. 5 1 .dx 5 4) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 5 The integral converges to J. 1 (x-4) OB. The improper integral diverges. dx = 5 Determine if the improper integral is convergent or divergent, and calculate its value if it is convergent. 15x20x -2 dx 2 Calculate the value of the improper integral. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. . 5x dx= 2 OB. The improper integral diverges. Evaluate the following integral using trigonometric substitution. dx x> 19 -361 What substitution will be the most helpful for evaluating this integral? A. x = 19 tan 0 B. x=19 sin 0 C. x=19 sec 0 Rewrite the given integral using this substitution. dx x-361 (Type an exact answer.) de Evaluate the following integral. 289 3 x-17x dx Find the partial fraction decomposition of the integrand. 289dx=10dx x-17x X-