a and b are +ve integers. a,-4,b form a geometric sequence, and -4,b,a form an arithmetric sequence.
(a) Find the value of ab.
(b) Find the values of a and b.
(c) (i) Find the sum to infinity of the geometric sequence a,-4,b,... .
(ii) Find the sum to infinity of all the terms that are +ve in the geometric sequence a,-4,b.
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
a and b are +ve integers. a,-4,b form a geometric sequence, and -4,b,a form an arithmetric sequence.
(a) Find the value of ab.
(b) Find the values of a and b.
(c) (i) Find the sum to infinity of the geometric sequence a,-4,b,... .
(ii) Find the sum to infinity of all the terms that are +ve in the geometric sequence a,-4,b.
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
i can get you a simple explanation here...
each next term of geometric sequence is MULTIPLIED by the common ratio 'r'
so, in general, terms are a,ar,ar^2,ar^3.....
when we have just 3 terms, we have a, ar, ar^2
for this (1st term * 3rd term) = (2nd term)^2 (you can check)
or if you don't want to remember the formula, you should know that difference between the terms is constant in arithmetic sequence
so, difference between b and -4 = difference between a and b
b - (-4) = a-b
you'll get same equation :)