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If you are given the sequence:     3 ; 12 ; 48 ; 192 ; 768 ; ...

a.    Find the 12th term of the sequence

b.    Find the sum of the first eight terms
in Mathematics by Diamond (39,212 points) | 128 views

1 Answer

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The sequence can be written as:   3 ; 3 x 4 = 12;    12 x 4 = 48;    48 x 4 = 192;    192 x 4 = 768

a.    It is a geometric sequence with a = 3  and r = 4;    ∴ Tn = ar^(n – 1)

T12 = 3 . 4^(121)

= 3. 4^11

= 3 x 4 194 304

= 12 582 912

b.    Sn = a(r^n - 1)/(r - 1)

S8 = 3(4^8 - 1)/(4 - 1)

= (4^8) - 1

= 65 535

by Diamond (39,212 points)

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