Question

all terms of an arithmetic sequence with common difference 4 are positive numbers.the product of 2 consecutive terms of this sequence is same as their sum​

Answer 1

Step-by-step explanation:

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.

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.

The two terms of the sequence are 6 and 10.