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MA1310 College Mathematics II

Module 1 Exercise 1.1 1. Describe an arithmetic sequence in two sentences.

A sequence in which each term after the first differs from the preceding term by a constant amount. The difference between consecutive terms is called the common difference of the sequence. 2. Describe a geometric sequence in two sentences.

A sequence in which each term after the first is obtained by multiplying the preceding term by a fixed nonzero constant. The amount by which we multiply each time is called the common ratio of the sequence. 3. Write the first four terms of the sequence. a1= 13 and an = an-1+8 for n ≥ 2 a1 = 13 a2 = an-1+8, (n = 2) a2 = 13 + 8 = 21 a3 = a2 + 8 a3 = 21 + 8 = 29 a4 = a3 + 8 a4 = 29 + 8 = 37

The first four terms of the sequence are 13, 21, 29, and 37 4. Evaluate: 16!2!*14!

16*15*14!2*1*14! = 16*15*14!2*1*14!

=16*152 = 2402

=120

5. Find the indicated sum i=15i2 i=15i2 = 12 + 22 + 32 + 42 + 52 = 1 + 4 + 9 + 16 +25 i=15i2 = 55 6. A company offers a starting yearly salary of $33,000 with a raise of $2,500 per year. Find the total salary over a 10-year period. an = a1 + (n - 1)*d, [where n = 10 years; a1 = $33,000; d = $2,500] a10 = 33,000 + (10 - 1) * 2,500 a10 = 33,000 + (9) * 2500 a10 = 33,000 + 22,500 a10 = 55,500

The total salary over a 10-year period will be $55,500.

7. Suppose you have $1 the first day of a month, $5 the second day, $25 the third day, and so on. That is, each day you save five times as much as you did the day before. What will you put aside for saving on the eighth day of the month?

1, 5, 25,…. r = 5, n = 1 an = 5n-1 a8 = 58-1 = 57 a8 = 78,125

The amount to put aside for saving on the eighth day of the month will be $78,125. 8. First 12 terms of the geometric sequence 2, 6, 18, 54,…

Common ratio (r) = 62 = 3, a1 = 2, n = 12 a5 = a4*r = 54*3 = 162 a6 = a5*r = 162*3 = 486 a7 = a6*r = 486*3 = 1,458 a8 = a7*r = 1458*3 = 4,374 a9 = a8*r = 4374*3 = 13,122 a10 = a9*r = 13122*3 = 39,366 a11 = a10*r = 39366*3 = 118,098 a12 = a11*r = 118098*3 = 354,294

The first 12 terms are 2, 6, 18, 54, 162, 486, 1,458, 4,374, 13,122, 39,366, 118,098, 354,294.…...

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