1. In a certain A.P the 24th term is twice the 10th term. Prove that 72nd term is twice the 34th
term. (3 marks)
Answers
Answer:
The nth term of an A.P is given by
a
n
=a
1
+(n−1)d…..eq(1)
where a
1
is the first term of A.P
and d is the common difference
hence 10th term of an A.P is
a
10
=a
1
+(10−1)d
a
10
=a
1
+9d…...eq(2)
and 24th term is a
24
a
24
=a
1
+(24−1)d
a
24
=a
1
+23d
given that the 24th term is twice the 10th term
⟹a
24
=2×a
10
⟹2×a
10
=a
1
+23d…..eq(3)
put value of a
10
from eq(2)
⟹2×(a
1
+9d)=a
1
+23d
⟹2a
1
+18d=a
1
+23d
⟹2a
1
−a
1
=23d−18d
⟹a
1
=5d.....eq(4)
now 34th term of A.P is given by
a
34
=a
1
+(34−1)d
put value of a
1
from eq(4) in above equation.
a
34
=5d+(33)d
a
34
=38d…...eq(5)
now 72nd term of A.P is given by
a
72
=a
1
+(72−1)d
put value of a
1
from eq(4) in above equation.
a
72
=5d+(71)d
a
72
=76d
a
72
=2×38d
we know that from eq(5)
a
34
=38d
hence, a
72
=2×a
34
Step-by-step explanation:
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