Use the table feature of a graphing utility to find the firs

Use the table feature of a graphing utility to find the first 10 terms of the sequence. (Assume n begins with 1.) a_n = 18 + 2 n a_1 = a_2 = a_3 = a_4 = a_5 = a_6 = a_7 = a_8 = a_9 = a_10 = Find the sum of the finite arithmetic sequence. -11 + (-7) + (-3) +1 + 5 + 9

Solution

1) an = 18 + 2n

a1 = 18 + 2*1 = 20

a2 = 18 + 2*2= 22

a3 = 18 + 2*3 = 24

a4 = 18+ 2*4 = 26

a5 = 18+ 2*5 = 28

a6 = 18+ 2*6 = 30

a7 = 18 + 2* 7 = 32

a8 = 18+ 2*8 = 34

a9 = 18+ 2*9 = 36

a10 = 18+ 2*10 = 28

or

[ after finding some terms we found that this is an A.P series with common difference 2, so you can directly add 2 to previous term to find next term ]

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2) - 11 + ( -7) + ( -3) + 1 + 5+ 9

here d = common difference = - 7 - ( -11) = 4

a = first term = - 11

n = no of terms = 6

so sum of these 6 terms by formula , Sn = (n/2) [ 2a + ( n-1)*d]

S6 = ( 6/2) [ 2*( -11) + ( 6-1) *4]

= -6