Write the general term of the geometric sequence, then use the formula to find a 7

ttyme411gl

ttyme411gl

Answered question

2022-07-02

Write the general term of the geometric sequence, then use the formula to find a 7 . Assume the sequences start at a 0 .
( a ) 3 , 15 , 75 , 375 , . . .
( b ) 18 , 6 , 2 , 2 3 , . . .
( c ) 0.0004 , 0.004 , 0.04 , 0.4 , . . .
( d ) 5 , 1 , 1 5 , 1 25

Answer & Explanation

Wade Atkinson

Wade Atkinson

Beginner2022-07-03Added 12 answers

General term of the geometric sequence: a n = a r n 1

1)Given: 3 , 15 , 75 , 375 ,
a = 3, r = 15 3 = 5
Thus,
a 7 = 3 ( 5 ) 7 1
= 3 ( 5 ) 6
= 3 ( 15625 )
= 46875

2)Given: 18 , 6 , 2 , 1 3 ,
a = 18, r = 6 18 = 1 3
Thus,
a 7 = 18 ( 1 3 ) 7 1
= 18 ( 1 3 ) 6
= 18 ( 1 3 6 )
= 18 ( 1 729 )
= 2 81

3) Given: 0.0004 , 0.004 , 0.04 , 0.4 ,
a = 0.0004, r = 0.004 0.0004 = 10
Thus,
a 7 = 0.0004 ( 10 ) 7 1
= 0.0004 ( 10 ) 6
= 400
Frederick Kramer

Frederick Kramer

Beginner2022-07-04Added 7 answers

(d) 5 , 1 , 1 5 , 1 25
First term is a = 5
Common ratio is r = 1 5
Formula for the geometric sequences: a n = a r n 1

a 7 = 5 ( 1 5 ) 7 1
a 7 = 5 ( 1 5 ) 6
a 7 = 5 ( 1 5 6 )
a 7 = 1 3125

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