28.If the 5th term of an A.P is 10 and the sum of 4th and 8th terms is 30,then find the
A.P.
Answers
Answer:
The nth term of an A.P is given by
a
n
=a
1
+(n−1)d
4th term of A.P is given by
a
4
=a
1
+(4−1)d
a
4
=a
1
+3d...eq(1)
8th term of A.P is given by
a
8
=a
1
+(8−1)d
a
8
=a
1
+7d...eq(2)
given that sum of 4th and 8th term is 24 ⟹a
4
+a
8
=24
from eq(1) and eq(2)
a
1
+3d+a
1
+7d=24
⟹2a
1
+10d=24…...eq(3)
6th term of A.P is given by
a
6
=a
1
+(6−1)d
a
6
=a
1
+5d...eq(4)
10th term of A.P is given by
a
10
=a
1
+(10−1)d
a
10
=a
1
+9d...eq(5)
given that sum of 6th and 10th term is 34 ⟹a
6
+a
10
=34
from eq(4) and eq(5)
a
1
+5d+a
1
+9d=34
⟹2a
1
+14d=34…...eq(6)
substract eq(3) by eq(6) we get
⟹2a
1
−2a
1
+14d−10d=34−24
⟹4d=10
⟹d=
4
10
⟹d=
2
5
...…..eq(7) common difference.
put value of d=2.5 in eq(3) we get
⟹2a
1
+10×2.5=24
⟹2a
1
+25=24
⟹2a
1
=24−25
⟹2a
1
=−1
⟹a
1
=−
2
1
= first term of A.P