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 = -5, 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. {S_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_ k = 1^12 2 2 10 12 24 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 + ... + 6n = 3n(n + 1) obeys Condition II of the Principle of Mathematical Induction, that is, if the formula is true for some natural number k, it is also true for the next natural number k + 1?

Solution

8) OPTION A

an = a(n - 1) – 3

a1 = 1

a2 = a1 – 3 = -2

a3 = a2 – 3 = -5

a4 = a3 – 3 = -8

10) Sum of sequence = 2 as 2 is constant.