Sequence and Series 83 Difficulty Level: B
6
(a) If a is A. M. between b and c, b is G. M. between a and c, then
prove that c will be H. M. between a and b.
(b) If a, b, c be in A. P., b, c, a in H. P., then show that c, a, b are in
G. P.
(c) Show that bº is greater than, equal to or less than ac according as
a, b, c are in A. P., G. P. and H. P.
If b + c, c + a, a + b are in H. P. then show that a, b, c are in
A. P.
[CTEVT 2074]
le
Prove that a, b, care in G. P. or in H. P. according as
a-ba
b-cb
>
a
or

yo answer should be 6 if im not mistaken

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for