Question

If sr denotes the sum of r terms of an ap and sa/a^2

Answer 1

The complete question is,

If Sr denotes the sum of r terms of an AP and Sa/a^2 = Sb/b^2 = c then express Sc in terms of a, b and c.

Given:

Sr denotes the sum of r terms of an AP and Sa/a^2 = Sb/b^2 = c

To find:

Express Sc in terms of a, b and c.

Solution:

The sum of r terms in an A.P. is given by,

Sr = r/2 [ 2A + (r - 1)D ]

where, A = first term

D = common difference

From given, we have,

Sa/a^2 = Sb/b^2 = c

Now consider,

Sa/a^2 = c

{a/2 [ 2A + (a - 1)D ]}/a^2 = c

[ 2A + (a - 1)D ]/2a = c

2A + (a - 1)D = 2ac ........(1)

Now consider,

Sb/b^2 = c

Similarly, we get,

2A + (b - 1)D = 2bc ........(2)

solving equations (1) and (2), we get,

A = c and D = 2c

Now,

Sc = c/2[2A + (c - 1)D]

= c/2 [2c  + (c - 1) 2c]

= c/2 [2c  + 2c² - 2c]

= c/2 × 2c²

∴ Sc = c³

Answer 2

Answer:

dont   know

Step-by-step explanation: