Sequences and Series Problems

Problem 1: For the sequence $76.19, $75.62, $75.05, $74.48, .......
2A. Find the explicit formula (general rule) for the general term an of the sequence
given above. and Use your explicit formula to find the 2001st term of the given
sequence.
Ans)
a2−a1=−$ 0.57
a3−a2 =−$ 0.57
a4−a3=−$ 0.57
Therefore it has a common difference d=−$ 0.57
So it is an Arithmetic Progression,
an=a1 + ( n−1 ) d
a2001=a1+ 2000× ( −$ 0.57 ) =$ 76.19−$ 1140=−$ 1063.81
2B. Find S2001 which is the sum of the first 2001 terms of the given sequence.
Ans)
Sn= n
2 [2 a1 + ( n−1 ) d ]
S2001=2001
2 [2 ( $ 76.19 ) + ( 2000 ) (−$ 0.57 ) ]=−$ 988,113.81
Problem 2. For the sequence 12000, 4800, 1920, 768, ....
2A. Find the explicit formula (general rule) for the general term an of the sequence
given above and calculate the 10th term of sequence.
Ans)
a2
a1
=0.4
a3
a2
=0.4