ar5 = 160
ar8 = 1280
so r3 = 1280/160 = 8 and so r = 2
then, ar5 = 160 gives a = 160/32 = 5
First term = a = 5
Common ratio = r = 2
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 }.
The nth term of the series is [ 4/2(n-1) ].
A geometric series represents the partial sums of a geometric sequence. The nth term in a geometric series with first term a and common ratio r is:T(n) = a(1 - r^n)/(1 - r)
Find the 7th term of the geometric sequence whose common ratio is 1/2 and whose first turn is 5
11.27357
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 }.
Divide any term, except the first, by the term before it.
In an arithmetic progression the difference between each term (except the first) and the one before is a constant. In a geometric progression, their ratio is a constant. That is, Arithmetic progression U(n) - U(n-1) = d, where d, the common difference, is a constant and n = 2, 3, 4, ... Equivalently, U(n) = U(n-1) + d = U(1) + (n-1)*d Geometric progression U(n) / U(n-1) = r, where r, the common ratio is a non-zero constant and n = 2, 3, 4, ... Equivalently, U(n) = U(n-1)*r = U(1)*r^(n-1).
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.
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.
The nth term of the series is [ 4/2(n-1) ].
In an arithmetic progression the difference between each term (except the first) and the one before is a constant. In a geometric progression, their ratio is a constant.That is,Arithmetic progressionU(n) - U(n-1) = d, where d, the common difference, is a constant and n = 2, 3, 4, ...Equivalently,U(n) = U(n-1) + d = U(1) + (n-1)*dGeometric progressionU(n) / U(n-1) = r, where r, the common ratio is a non-zero constant and n = 2, 3, 4, ...Equivalently,U(n) = U(n-1)*r = U(1)*r^(n-1).
A geometric series represents the partial sums of a geometric sequence. The nth term in a geometric series with first term a and common ratio r is:T(n) = a(1 - r^n)/(1 - r)
Find the 7th term of the geometric sequence whose common ratio is 1/2 and whose first turn is 5
It appears to have been Svante Arrhenius (1859-1927) in 1896, a Swedish scientist who developed what is now know as the 'greenhouse gas law':"if the quantity of carbonic acid increases in geometric progression, the augmentation of the temperature will increase nearly in arithmetic progression"
11.27357
It is 1062882.