There are 5 common differences between seventh and twelfth terms, so the CD is 2.5/5 ie 0.5. First term is therefore 15 - 6 x 0.5 = 12.
-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.
First, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth, eleventh, twelfth.
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).
If a is the first term and r the common difference, then the nth term is tn = a * (n-1)r So t16 = a + 15r Then 6*t16 = 6(a + 15r) or 6a + 90r No further simplifiaction is possible.
-4 is the first negative term. The progression is 24,20,16,12,8,4,0,-4,...
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 }.
It is an Arithmetic Progression with a constant difference of 11 and first term 15.
RAMANUJANRAMANUJAN
You can use one of the formulae for the sum of an arithmetic progression to calculate that.
First, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth, eleventh, twelfth.
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).
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).
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"
35 minus 4 differences, ie 4 x 6 so first term is 11 and progression runs 11,17,23,29,35...
They are both adjectives. The first relates to geometry and the second to arithmetic.