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How do you write the expression for the nth term of the geometric sequence #a_1=1000, r=1.005, n=60#?

Answer 1

Elijah Allen

#a_n=1000xx1.005^n# and for #n=60#, #a_60=1348.85#

In a geometric sequence, where first term is #a_1# and common ratio is #r#,

#n^(th)# term #a_n# is given by #a_1xxr^(n-1)#

Hence #n^(th)# term of a geometric sequence whose first term is #a_1=1000# and common ratio is #r=1.005# is

#a_n=1000xx1.005^n#

and #a_60=1000xx1.005^60~=1000xx1.34885=1348.85#,

where value of #1.005^60# has been approximated up to #5dp#.

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Answer 2

Xavier Alonso

The expression for the nth term of a geometric sequence is given by:

[ a_n = a_1 \times r^{(n-1)} ]

Substituting the given values:

[ a_n = 1000 \times (1.005)^{59} ]

[ a_n ≈ 1081.47 ]

Therefore, the expression for the 60th term of the geometric sequence with ( a_1 = 1000 ) and ( r = 1.005 ) is approximately ( 1081.47 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.