How many terms are there in each of the sequences? 1) 1 , 3 , 9 , 27 ,

rjawbreakerca

rjawbreakerca

Answered question

2022-07-09

How many terms are there in each of the sequences?
1) 1 , 3 , 9 , 27 , 81 , 243 , . . . , 6561
2) 1 , 4 , 4 2 , 4 3 , . . . . , 4 50
3) 1000 , 2000 , 3000 , 4000 , . . . , 20000

Answer & Explanation

Leslie Rollins

Leslie Rollins

Beginner2022-07-10Added 25 answers

1) Given 1 , 3 , 9 , 27 , 81 , 243 , . . . , 6561
This is a geometric sequence with first term 1 and common ratio 3, last term of the sequence is 6561.
Formula for the n-th term
a n = a r n 1
Thus, we have:
6561 = 1 ( 3 ) n 1
3 n 1 = 3 8
n 1 = 8
n = 9
Thus, there are 9 terms in the sequence.

2) Given 1 , 4 , 4 2 , 4 3 , . . . . , 4 50
The sequence is geometric with first term 1 and common ratio 4, the last term of the sequence is 4 50
Formula for geometric sequence
a n = a r n 1
4 50 = 1 ( 4 ) n 1
4 n 1 = 4 50
n 1 = 50
n = 51
Thus, there are 51 terms in the sequence
Cristopher Knox

Cristopher Knox

Beginner2022-07-11Added 6 answers

(3) 1000 , 2000 , 3000 , 4000 , . . . , 20000
Arithmetic sequence
a = 1000
d = 1000
Last term = 20000
a + ( n 1 ) d = a n
1000 + ( n 1 ) 1000 = 20000
( n 1 ) 1000 = 19000
n 1 = 19
n = 20
Number of terms in this sequence is 20.

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