Sequences :)

Question

Find the 5th,50th, and nth term of the arithmetic sequences

1) 3,5,7...

5th...13 is it correct ?

50th...103 is it correct ?

Nth...??? I have no idea how to find this

2) a1=2.1, a3=4.7

5th...?

50th...?

Nth...?

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Find the 6th, and nth term of the GEOMETRIC sequences

3) 1,2,4

6th...is it 65,536 ?

Nth...?

4) a1=3, a3=48

6th...?

Nth...? 

Thanks ??  

Answer 1

1) 3,5,7,9,11,13,15,...

    use the formula x(n)=a+d(n-1) where a=1st term, d=difference between terms, n=term #

    x(5)=3+2(5-1)

    x(5)=3+2(4)

    x(5)=3+8=11

 

    x(50)=3+2(50-1)

    x(50)=3+2(49)

    x(50)=3+98=101

 

    x(n)=3+2(n-1)

    x(n)=3+2n-2

    x(n)=2n+1 is the Nth term

 

2)  2.1, ?, 4.7,...

     4.7-2.1=2.6, 2.6/2=1.3(d=1.3)

     2.1+1.3=3.4

     2.1, 3.4, 4.7, 6, 7.3, ...

    x(5)=2.1+1.3(5-1)

    x(5)=2.1+1.3(4)

    x(5)=2.1+5.2=7.3

 

    x(50)=2.1+1.3(50-1)

    x(50)=2.1+1.3(49)

    x(50)=2.1+63.7=65.8

 

    x(n)=2.1+1.3(n-1)

    x(n)=2.1+1.3n-1.3

    x(n)=1.3n+0.8

  

The geometric sequence problems are done by Parviz F.

 

Answer 2

This is the sequence of odd numbers, excluding 1 .

 

  3, 5, 7, .... , 2n +1,

 

  5th term : 2( 5 ) +1 = 11    / 3,5, 7, 9, 11 .,,,,,

 

 50th : n = 50     2(n+1) = 2 ( 50 +1) = 102

 

Nth :   2 N +1 

 

You have included 1 into sequence too , then had to count from 0 , where first term 2( 0 ) +1 equals 1.

 

3) :

      { a_n } ⁿ = { 1, 2, 4 , ...2^n-1, ....} 

               0

 

6th term :       2  ^{n -1} = 2 ⁵=  32     / { 1, 2, 4, 8, 16, 32, ......

 

4)

 

    { 3r⁰ , 3 r , 3 r², ....3r^{n -1}, ..}

 

    3 r² / 3 r ⁰ = 48/ 3 = 16  ,  r =4

 

    { 3 , 12, 48, ...... 3( 4 ^{n -1}) , ...... }

 

     6th term :

                   3 ( 4 ⁵ ) = 3072

 

          N th term :  3 ( 4 ^{N -1} )