The sequence is defined recursively Write the first four ter

The sequence is defined recursively. Write the first four terms. a_1 = 1, a_n = a_n - 1 = 3 a_1 = 1, a_2 = - 2, a_3 = - 3, a_4 = - 8 a_1 = 1, a_2 = 4, a_3 = 7, a_4 = 10 a_1 = - 3, a_2 = - 6, a_3 = - 9, a_4 = - 12 a_1 = 1, a_2 = 0, a_3 = - 3, a_4 = - 6 A geometric sequence is given. Find the common ratio and write out the first four terms (a_n) = [4^n] r = 4; s_1 = 4, s_2 = 16, s_3 = - 64, s_4 = 256 r = 4; s_1 = 4, s_2 = 8, s_3 = 12, s_4 = 16 r = 4n; s_1 = 4, s_2 = 16, s_3 = 64, s_4 = 256 r = 4n; s_1 = 4, s_2 = 8, s_3 = 12, s_4 = 16 Find the sum of the sequence. Sigma^12_k = 1 2 2 10 12 24 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n, Does the following formula 6 + 12 + 18 + TripleDot + 6n = 3n(n + 1) obeys Condition II of the Principle of Mathematical Induction, that is, if the formula is true for same natural number k, it is also true for the next natural number k + 1? Choose your answer appropriately, No, that is, the formula is true for some natural number k does not imply that it is also true for the next natural number k + 1, Yes, that is, the formula is true for some natural number k implies that it is also true for the next natural number k + 1. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the Binomial Theorem to find the indicated coefficient or term. The 5th term in the expansion of (3x + 2)^5 160 360x^2 120x 240x Find the sum. 1 + 3 + 5 + TripleDot + 203 10, 404 10, 201 10, 609 10, 506 Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given a = 5; r = 4 pi a_5 = 5 + 16 pi, a_n = 5 + 4 pi(n - 1) a_5 = 1280 pi^4, a_n = 5 middot 4^n - 1 pi^n - 1 a_5 = 5120 pi^5, a_n = 5 middot 4^n pi^n a_5 = 1280 pi, a_n = 5 middot 4^n - 1 pi

Solution

12) (3x+2)^5= 243x^5 + 810x^4 + 1080x^3 + 720x^2 + 240x + 32

Answer = 240x

13) As 1+3+5+...+(2n-1) = n²

   ^Here 1+3+5+...+(102^2 -1) = 102² = 10404