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Problem 1:

The first, second, and the nth terms of an arithmetic sequence are 2, 6, and 58 respectively,

i.  Find the value of n

13

ii.  For that value of n, find the exact value of the sum of n terms.

(58 + 2) * (13 / 2) = 390

 

Problem 2: 

 

The seats in a theatre are arranged so that each row accommodates four people more than the previous row. If the first row seats 50 people, how many will the 9th row seat?

 Feb 25, 2019
 #1
avatar+19686 
+1

1   an = a1 +(n-1)d        a1 = 2    an = 58    d = 4

     58 = 2 +(n-1)(4)

      14 = n-1

       n = 15            For n= 13   a13 = 58-4-4= 50

 

Sn for arithmetic series =     (n (a1+an)/2)   =  15 ( 2+58)/2 ) =  450

 

For a13 sum     = n(a1+a13)/2 = 13 (2+50)/2 = 338

 Feb 25, 2019
edited by ElectricPavlov  Feb 25, 2019
edited by ElectricPavlov  Feb 25, 2019
edited by ElectricPavlov  Feb 25, 2019
 #2
avatar+19686 
+1

an = 50 + (n-1)d        d = 4

an = 9th row = 50 + (8)(4) = 82 people

 Feb 25, 2019

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