The nth term of the series is [ 4/2(n-1) ].
RAMANUJANRAMANUJAN
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 }.
It is neither. (-6) - (-2) = -4 (-18) - (-6) = -12 which is not the same as -4. Therefore it is not an arithmetic progression - which requires the difference between successive terms to be the same. Also -162/-54 = 3 -468/-162 = 2.88... recurring, and that is not the same as 3. Therefore it is not a geometric progression - which requires the ratio of terms to be the same.
Arithmetic : (First term)(last term)(act of terms)/2 Geometric : (first term)(total terms)+common ratio to the power of (1+2+...+(total terms-1))
2
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.
RAMANUJANRAMANUJAN
The sum to infinity of a geometric series is given by the formula Sā=a1/(1-r), where a1 is the first term in the series and r is found by dividing any term by the term immediately before it.
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 }.
a+a*r+a*r^2+...+a*r^n a = first number r = ratio n = "number of terms"-1
un = u0*rn for n = 1,2,3, ... where r is the constant multiple.
It is neither. (-6) - (-2) = -4 (-18) - (-6) = -12 which is not the same as -4. Therefore it is not an arithmetic progression - which requires the difference between successive terms to be the same. Also -162/-54 = 3 -468/-162 = 2.88... recurring, and that is not the same as 3. Therefore it is not a geometric progression - which requires the ratio of terms to be the same.
t(1) = a = 54 t(4) = a*r^3 = 2 t(4)/t(1) = r^3 = 2/54 = 1/27 and so r = 1/3 Then sum to infinity = a/(1 - r) = 54/(1 - 1/3) = 54/(2/3) = 81.
Arithmetic : (First term)(last term)(act of terms)/2 Geometric : (first term)(total terms)+common ratio to the power of (1+2+...+(total terms-1))
2
Right angle and rectangle are geometric terms.
This a progression that involves addition or subtraction of successive terms in a sequence.