All the terms of an Arithmetic Sequence with Common difference 4 are positive numbers . The product of two consecutive terms of this sequence is same as their Sum ?
(1) if one term is x , what is the next tem ? (2)Calculate those terms ?
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Question
The terms of an arithmetic sequence with common difference 4 are natural numbers.
a) If x is a term in this sequence, what is the next term?
b) If the sum of reciprocals of two consecutive terms of this sequence is 154, find those terms.
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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
Step-by-step explanation:
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Answer:
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
15
4
.
x
1
+
x+4
1
=
15
4
x
2
+4x
2x+4
=
15
4
30x+60=4x
2
+16x
4x
2
−14x−60=0
4x
2
−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.