Answer:
Sum of first and third term is = -3 + -12 = 15
sum of all the three terms is = -3 + 6 + -12 = -9
common difference = -2
Step-by-step explanation:
For the GP let the first term be a
and common ratio be r
n the term of gp is given by ar^(n-1)
then
first term = a
second term = ar^(2-1) = ar
third term = ar^(3-1) = ar^2
given, sum of the first two terms of a gp is 3
a + ar = 3
=> a(1+r) = 3 -------> 1
also , sum of the second and the third terms is-6
ar + ar^2 = -6
taking ar as common
=>ar(1+r) = -6
it can be also written as product of r and a(1+r)
=> r*a(1+r)= -6
we have calculated value of a(1+r) as 3, substituting this value here we have
=> r*3 = -6
=> r = -6/3 = -2
Thus, common difference is -2.
As a(1+r) = 3 , substituting value of r as -2 here, we have
a(1+(-2) = 3
=> a(-1)= 3
=> a = -3
Thus, first term is a = -3
second term is ar = -3*-2= 6
third term is ar^2 = -3*(-2)^2= -3*4 = -12
Sum of first and third term is = -3 + -12 = 15
sum of all the three terms is = -3 + 6 + -12 = -9
common difference = -2