Question

20. a)

I^ 2 -(. a 2 )^ 2 ,I^ 2 ,I^ 2 +( a 2 )^ 3

are three consecutive terms of an arithmetic sequence.

What is the common difference? b) Slant height of a square pyramid is / and the base edge is a. What is the length of lateral edge? What is its height? c) The height of a square pyramid is sqrt(15) centimetres and the lateral edge is

sqrt(19) centimetres. What is its slant height?


Please answer with steps​

Answer 1

Answer:

The terms of an arithmetic sequence with common difference 4 are natural numbers.

(a) Let x be a term of the sequence and y be the next term of the sequence.

Common difference =yx

4=yx

y=x+4

So the next term is x+4.

(b) Let x and x+4 be the two consecutive terms of sequence such that sum of their reciprocals is 154.

Step-by-step explanation:

x1+x+41=154

x2+4x2x+4=154

30x+60=4x2+16x

4x2−14x−60=0

4x2−24x+10x−60=0

4x(x−6)+10(x−6)=0

(4x+10)(x−6)=0

x=2−5 or x=6

But terms of the sequence are natural numbers.

∴x=6 and x+4=10.

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