What is the sum of the arithmetic series where n=100 , t1=7 and t2=205
So we know n=100, t1=7, t100=205,
We will use this formula to find the sum Sn=(n/2)(a1+tn) (There are many formulas to find the sum)
S100=(100/2)(7+205)
=10,600 the answer is 10,600.
Well, if I may calculate it for you while staying in character as Clown Bot, let's find the sum of this arithmetic series!
To find the sum, we can use the formula: S = (n/2)(t1 + tn), where S denotes the sum, n is the number of terms, t1 is the first term, and tn is the last term.
Here, n = 100, t1 = 7, and we need to find tn. To find tn, we can use the formula for the nth term of an arithmetic series: tn = t1 + (n - 1)d, where d is the common difference.
Given that t2 = 205, we can find d as follows:
t2 = t1 + d
205 = 7 + d
d = 198
Now that we know d, we can find tn:
tn = t1 + (n - 1)d
tn = 7 + (100 - 1)198
tn = 7 + 99(198)
tn = 7 + 19602
tn = 19609
Finally, we can substitute the values into the sum formula:
S = (n/2)(t1 + tn)
S = (100/2)(7 + 19609)
S = 50(19616)
S = 980,800
So, the sum of the arithmetic series is 980,800. That's quite the sum, but hey, don't clown around with numbers or else you might end up with a silly calculation!
To find the sum of an arithmetic series, we can use the formula:
S = (n/2)(t1 + tn)
Where:
- S represents the sum of the series,
- n is the number of terms in the series,
- t1 is the first term of the series,
- tn is the nth term of the series.
In this case, we are given n = 100, t1 = 7, and t2 = 205.
First, we need to find tn using the given information. Since t1 is the first term and t2 is the second term, we can determine the common difference (d) by subtracting t1 from t2:
d = t2 - t1
d = 205 - 7
d = 198
Now, we can find tn by substituting the values we have into the arithmetic formula:
tn = t1 + (n-1)d
tn = 7 + (100-1)(198)
tn = 7 + (99)(198)
tn = 7 + 19602
tn = 19609
Now, we can substitute the values for n, t1, and tn into the sum formula:
S = (n/2)(t1 + tn)
S = (100/2)(7 + 19609)
S = (50)(19616)
S = 980,800
Therefore, the sum of the arithmetic series with n = 100, t1 = 7, and t2 = 205 is 980,800.
if t1 = 7 and t2 = 205
then d = 205-7 = 198
sum(100) = (100/2)(2(7) + 99(198))
= 50(19616)
= 980800