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1. In a certain A.P the 24th term is twice the 10th term. Prove that 72nd term is twice the 34thterm. (3 marks) |
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Answer» 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
=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
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