If the 10th term of the arithmetic sequence having common difference 4 is 50, find the first term.
Answers
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
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.
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.