In a certain A.P. the 32nd term is twice the 12th term. Prove that 70th term is twice the 31st term.
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Answer:
Step-by-step explanation:
Solution :-
Let the 1st term be a and the common difference be d.
According to the Question,
a₃₂ = 2a₁₂
a + 31d = 2 (a + 11d)
a + 31d = 2a + 22d
a = 9d ...(i)
a₇₀ = a + 69d
a₇₀ = 9a + 69d = 78d [ Putting Eq (i) value]
a₃₁ = a + 30d
a₃₁ = 9d + 30d = 39d [ Putting Eq (i) value]
a₇₀ = 2a₃₁
Hence Proved.
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