Use the approach in​ Gauss’s Problem and find

Rubi Riggs

Rubi Riggs

Answered question

2022-04-11

Use the approach in​ Gauss’s Problem and find the sums of following arithmetic sequences
(a) 1+2+3+4++999
(b) 1+3+5+7++999
(c) 8+17+26+35++881
(d) 692+685+678+671++6

Answer & Explanation

phoenixtreeaung

phoenixtreeaung

Beginner2022-04-12Added 19 answers

(a) 1+2+3+4++999
Here, first term a0=1, a1=2, a2=3
d=a1a0=21=1
Thus, it's an arithmetic sequence
an=a0+(n1)d
999=1+(n1)(1)
998=n1
n=999
Sum of the series: Sn=n2[]2a+(n1)d
Sn=9992[2+998]
Sn=499500
(b) 1+3+5+7++999
a0=1, a1=3, a2=5, an=999
d=a1=a0=31=2
Thus, the sequence is arithmetic
999=1+(n1)2
=9982=n1
n=500
The sum of sequence: Sn=5002[2+499×2]
Sn=250000
(c) 8+17+26+35++881
a0=8, a1=17, an=881
d=178=9
881=8+(n1)(9)
n1=88189
n=97
The sum of sequence: Sn=972[2(8)+96(9)]
Sn=42680
davelucasnp0j

davelucasnp0j

Beginner2022-04-13Added 16 answers

4) Given: 692+685+678+671++6
We have: a0=692, d=685692=7
an=6
an=a0+(n1)d
6=692+(n1)(7)
n=99
Sn=n2[2a0+(n1)d]
Sn=992[2(692)+98(7)
Sn=34551

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