Question

the ratio of 5th term to 12th term is 6:13. Find the ratio of 10th term to 6th term​

Answer 1

Answer:

$\large{\underline{\boxed{\sf Ratio = 11:7}}}$

Step-by-step explanation:

We know that ;

aₙ = a + (n - 1)d

Where,

• n = no. of terms
• a = first term
• d = common difference

Now,

a₅ = a + 4d

a₁₂ = a + 11d

It is given that the ratio of 5th term and 12th term is 6:13.

$\tt \frac{a + 4d}{a + 11d} = \frac{6}{13} \\ \\ \bf on \: cross - multiplying : \\ \\ \tt 13(a + 4d) = 6(a + 11d) \\ \\ \tt 13a + 52d = 6a + 66d \\ \\ \tt 13a - 6a = 66d - 52d \\ \\ \tt 7a = 14d \\ \\ \tt a = \frac{14d}{7} \\ \\ \implies \tt a = 2d$

We need to find, the ratio of 10th and 6th term.

a₁₀ = a + 9d

a₆ = a + 5d

$\tt \implies \frac{a + 9d}{a + 5d} \\ \\ \tt \implies \frac{2d + 9d}{2d + 5d} \\ \\ \tt \implies \frac{11d}{7d} \\ \\ \tt \implies \frac{11}{7} = 11:7$

Hence, the required ratio is 11:7.

Answer 2

$\mathsf{\red{\huge{\underline{\boxed{Answer=11:7}}}}}$

$\rule{200}{2}$

$\mathfrak{\underline{\underline{\blue{\large{Explanation}}}}}$

We know,

an = a + (n-1)d

So, we have :-

a5 = a + (5-1)d

a5 = a + 4d........(i)

_____________

a12 = a + (12-1)d

a12 = a + 11d

______________________

A. T.Q

» a+4d / a +11d = 6/13

Cross Multiply

» 13(a+4d)=6(a+11d)

» a = 14d/7

» a = 2d

We have to find ratio of 10th and 6th term

a10 = a +9d

a6 = a + 5 d

__________________

A. T. Q

» a + 9d / a+5d

-----------( Put value of a)

» 2d +9d/2d+5d

» 11d / 7d

» 11/7

» 11:7

_________[ Answer]

$\rule{200}{2}$

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