Problem 3 Using the Arithmetic Mean

GRIDDED RESPONSE

What is the missing term of the arithmetic sequence … , 15 , □ , 59 , … ? dot dot dot comma 15 comma white square comma 59 comma dot dot dot question mark

arithmetic mean  = 15 + 59 2 = 37 arithmeticmean . equals . fraction 15 plus 59 , over 2 end fraction . equals 37

The missing term is 37.

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3. 1. The 9th and 11th terms of an arithmetic sequence are 132 and 98. What is the 10th term?
   2. Reasoning If you know the 5th and 6th terms of an arithmetic sequence, how can you find term 7 using the arithmetic mean?

Problem 4 Using an Explicit Formula for an Arithmetic Sequence

Sports Arena The numbers of seats in the first 13 rows in a section of an arena form an arithmetic sequence. Rows 1 and 2 are shown in the diagram below. How many seats are in Row 13?

• Step 1 Find the common difference.

  d = a 2 − a 1 = 16 − 14 = 2 d equals , eh sub 2 , minus , eh sub 1 , equals 16 minus 14 equals 2

• Step 2 Write an explicit formula for the arithmetic sequence.

  a n = a + ( n − 1 ) d Use the explicit formula . a 13 = 14 + ( 13 − 1 ) 2 Substitute  13  for  n , 14  for  a , and  2  for  d .   = 38 Simplify . table with 3 rows and 3 columns , row1 column 1 , eh sub n , column 2 equals eh plus . open , n minus 1 , close . d , column 3 cap usetheexplicitformula . . , row2 column 1 , eh sub 1 3 , column 2 equals 14 plus . open , 13 minus 1 , close . 2 , column 3 cap substitute . 13 , for , n comma 14 , for , eh comma , and , 2 , for , d . , row3 column 1 , , column 2 equals 38 , column 3 cap simplify , . , end table

  There are 38 seats in Row 13.

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4. The numbers of seats in the first 16 rows in a curved section of another arena form an arithmetic sequence. If there are 20 seats in Row 1 and 23 seats in Row 2, how many seats are in Row 16?