The sum of the first 50 terms of an arithmetic series is 100. If the common differenc is 2, what is the first term?
i keep getting -23 but its not right......... :(
i keep getting -23 but its not right......... :(
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The sum of an arithmetic sequence is given by
Sn= n[(a1 +an)/2]
100= 50 [(a1 + an)/2]
a1=2 + a0
an=100+a0
100= 50 [102+2a0)/2]
2=[(102+2a0)/2]
4=102 + 2a0
-98=2a0
a0=-49
so add 2 to that and u get
a1=-47
an=dn+a0
an=2(n)-49
a0= the term before a1
Sn= n[(a1 +an)/2]
100= 50 [(a1 + an)/2]
a1=2 + a0
an=100+a0
100= 50 [102+2a0)/2]
2=[(102+2a0)/2]
4=102 + 2a0
-98=2a0
a0=-49
so add 2 to that and u get
a1=-47
an=dn+a0
an=2(n)-49
a0= the term before a1
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Use Sn=n/2(2a+(n-1)d)
Now, sub in what you know. You know the sum (Sn) =100, and that the difference is 2 (d). You also know that n (the number of terms) is 50.
100=50/2(2a+(50-1)2)
100=25(2a+98)
100=50a+2450
-2350=50a
a=-47
Now, sub in what you know. You know the sum (Sn) =100, and that the difference is 2 (d). You also know that n (the number of terms) is 50.
100=50/2(2a+(50-1)2)
100=25(2a+98)
100=50a+2450
-2350=50a
a=-47