Question

if 70th term is of ap is 0 then the ratio of 31st and 57th term is​

Answer 1

Answer:-

Given:-

70th term of an AP = 0

We know that,

nth term of an AP(aₙ) = a + (n - 1)d

So,

⟹ a + (70 - 1)d = 0

⟹ a + 69d = 0

⟹ a = - 69d -- equation (1).

We have to find:-

Ratio of 31st & 57th terms.

• a₃₁ = a + (31 - 1)d = a + 30d
• a₅₇= a + (57 - 1)d = a + 56d

Hence,

⟹ a₃₁ : a₅₇ = (a + 30d) : (a + 56d)

Substitute a = - 69d from equation (1).

⟹ a₃₁ : a₅₇ = ( - 69d + 30d) : (- 69d + 56d)

⟹ a₃₁ : a₅₇ = ( - 39d) : ( - 13d)

⟹ a₃₁ : a₅₇ = 39 : 13

⟹ a₃₁ : a₅₇ = 3 : 1

Answer 2

Answer:

❍ Given :

• if 70th term is of ap is 0 then the ratio of 31st and 57th term is.

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❍ To Find :

• 31st and 57th term is?

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❍ Solution :

We know that,

☄nth term of an AP ( aᵑ) = a + ( n - 1) d

So,

$\mathsf\blue{ \implies \:a + (70 - 1)d = 0 }$

$\mathsf\blue{ \implies \:a + 69d = 0 }$

$\mathsf\blue{ \implies \: (equation \: 1)}$

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Then, find it

☄Ratio of 31st & 57th term.

• a₃₁ = a+ ( 31 - 1 )d = a + 30d
• a₅₇ = a + ( 57- 1)d = a+ 56d

now,

• ➵a₃₁ : a₅₇ = ( a+ 30d) : ( a + 56d)
• ➵a₃₁ : a₅₇ = ( -69d + 30d) : (-69d + 56d)
• ➵a₃₁ : a₅₇ = ( -39d ) : ( -13d )
• ➵a₃₁ : a₅₇ = 39 : 13

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❍ Hence,

➵a₃₁ : a₅₇ = 39 : 13