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∙ 10y agoU5 = a + 4d = 5
U7 = a + 6d = 3
Subtracting the first equation from the second gives
2d = -2 therefore d = -1
and then a + 4d = 5 implies that a = 9.
So Sn = n/2*{2a + (n-1)*d}
thus S10 = 10/2*{18 + 9*(-1)}
= 5*{9} = 45
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∙ 10y agoThis question is impossible to answer without knowing the difference between successive terms of the progression.
Any number you like. You need two terms to uniquely identify an arithmetic progression.
It is not possible to answer this question without information on whether the terms are of an arithmetic or geometric (or other) progression, and what the starting term is.
-4 is the first negative term. The progression is 24,20,16,12,8,4,0,-4,...
It is an Arithmetic Progression with a constant difference of 11 and first term 15.
This question is impossible to answer without knowing the difference between successive terms of the progression.
2
A harmonic sequence is a sequence of numbers in which the reciprocal of each term forms an arithmetic progression. In other words, the ratio between consecutive terms is constant when the reciprocals of the terms are taken. It is the equivalent of an arithmetic progression in terms of reciprocals.
Any number you like. You need two terms to uniquely identify an arithmetic progression.
It is not possible to answer this question without information on whether the terms are of an arithmetic or geometric (or other) progression, and what the starting term is.
For an Arithmetic Progression, Sum = 15[a + 7d].{a = first term and d = common difference} For a Geometric Progression, Sum = a[1-r^15]/(r-1).{r = common ratio }.
-4 is the first negative term. The progression is 24,20,16,12,8,4,0,-4,...
The formula for the sum of the first n terms of an arithmetic progression is Sn = n/2 * (a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term.
In an arithmetic progression (AP), each term is obtained by adding a constant value to the previous term. In a geometric progression (GP), each term is obtained by multiplying the previous term by a constant value. An AP will have a common difference between consecutive terms, while a GP will have a common ratio between consecutive terms.
85 (=17*5). The middle term is 5. There are 8 terms bigger than 5 and 8 smaller. The term smaller than 5 and next to it is 5 - r The term bigger than 5 and next to it is 5 + r So these two average 5. Similarly, the next pair outwards average 5; and so on. So the sum of the progression is equivalent to the sum of 8 pairs of numbers whose average is 5 and the middle term which is 5 ie 17 lots of 5.
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It is an Arithmetic Progression with a constant difference of 11 and first term 15.