How many terms are there in each of the sequences? a . 56 , 57 , 58 ,

Aedan Gonzales

Aedan Gonzales

Answered question

2022-05-13

How many terms are there in each of the sequences?
a . 56 , 57 , 58 , 59 , . . . , 456
b .1 , 5 , 5 2 , 5 3 , . . . , 5 40
c . 100 , 200 , 300 , 400 , . . . , 40000
d . 1 , 3 , 9 , 27 , 81 , 243 , . . . , 6561

Answer & Explanation

parentalite50bqd

parentalite50bqd

Beginner2022-05-14Added 12 answers

a . 56 , 57 , 58 , 59 , . . . , 456
Apply this formula: a n = a 0 + ( n 1 ) d
a 0 = f i r s t   t e r m = 56
d = c o m m o n   d i f f e r e n c e = 1
a n = l a s t   t e r m = 456
Thus,
456 = 56 + ( n 1 ) 1
456 = 56 + n 1
456 56 = n 1
400 = n 1
n = 401
Therefore, there are 401 terms
b .1 , 5 , 5 2 , 5 3 , . . . , 5 40
Apply the formula: a n = a r n 1
a = f i r s t   t e r m = 1
r = c o m m o n   r a t i o = 5
a n = l a s t   t e r m
Thus, we have
5 40 = ( 1 ) ( 5 ) n 1
5 40 = 5 n 1
n 1 = 40
n = 41
Thus, there are 41 terms
London Ware

London Ware

Beginner2022-05-15Added 3 answers

c ) 100 , 200 , 300 , 400 , . . . , 40000
Formula: a n = a 0 + ( n 1 ) d , where
a 0 = 100
d = 100
a n = 40000
So,
40000 = 100 + ( n 1 ) 100
40000 = 100 m
n = 40000 100
= 400

d ) 1 , 3 , 9 , 27 , 81 , 243 , . . . , 6561
Formula: a n = a r n 1 , where
a = 1
r = 3
a n = 6561
Hence,
3 8 = ( 1 ) ( 3 ) n 1
3 8 = 3 n 1
n 1 = 8
n = 9

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