Common difference | Mathematics homework help

·         Formulas:

1.    Find the common difference of the sequence 2, 7, 12, 17, 22, … What is the common difference ?

2.    Find the 31^st term in the sequence whose general term is a_n = -3 + 4(n – 1).

3.    What is the common ratio for the geometric sequence –¹⁄₃ , ¹⁄₆ , –¹⁄₁₂ …

4.    Find the 12^th term of the sequence a_n = n(n – 6).

5.    Find the 4^th term of the sequence a_n = 1000 (0.1)^n-1

6.    Given the geometric sequence -2, 6, -18, … find the next term

7.    Given that the first term of a geometric sequence is -320 and seventh term is -3645, the common ratio to the nearest tenth is?

8.    What is the first term in the arithmetic sequence __ , 0, __ , 30, 45

9.    The fifth term of a geometric sequence is ¹⁄₁₀₈ and the common ratio is ¹⁄₃. The first term to this is?

10.What is the common ratio in the sequence 12, -18, 27, …

Rewrite the following series in summation notation in #s 11 & 12.

11.3 + 12 + 48 + 192 + 768

12.7 + 12 + 17 + 22 + 27 + 32

Evaluate each series using sum formulas.

13.4 + 12 + 20 + 28 + …; n = 9 ie the sum of the 1^st nine terms

14.3 + 6 + 12 + 24 + …; n = 8 ie the sum of the 1^st eight terms

Expand each series and evaluate.

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18.Find the two-hundredth term of the sequence: 1, 5, 9, 13, . . . .

19.A partial sum of the arithmetic series is given. Find the sum: 3 + 5 + 7 + . . .+ 101.

20.Determine whether the series 3 – 1 + ¹⁄₃ – ¹⁄₉ + … is convergent or divergent. If convergent, find its sum.