Question

For what value of n are the nth terms of aps:63,65,67......and3,10,17....equal?​

Answer 1

Step-by-step explanation:

Let the 1st AP be A =63,65,68.....

Let the 2nd AP be B = 3,7,17......

For A , common difference is : 65-63 = 2

For B ,common difference is : 10-3 = 7

Now Let the nth term be An and Bn respectively.

According to question

An = Bn

=> 63+(n-1)2 = 3+(n-1)7

=>60 + 2n-2 = 7n-7

=>65 = 5n

=> n = 13

Thus 13th term of both AP's will be same

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Answer 2

$\bf{\underline{Solution}}:-$

$\bf\dag{\underline\orange{{{For\:First\:AP}}}}$

• First term (a) = 63

• Common difference (d) = 65 - 63 = 2

Now,

we know that,

$\orange{\bigstar}\:\:{\underline{\boxed{\bf\purple{a_n=a+(n-1)d}}}}$

$\rm\longrightarrow\:a_n=63+(n-1)\times{2}$

$\rm\longrightarrow\:a_n=63+2n-2$

$\rm\longrightarrow\:a_n=61+2n$

$\bf\dag{\underline\green{{{For\:second\:AP}}}}$

• First term (a) = 3

• Common difference (d) = 10 - 3 = 7

Now,

we know that,

$\blue{\bigstar}\:\:{\underline{\boxed{\bf\pink{a_n=a+(n-1)d}}}}$

$\rm\longrightarrow\:a_n=3+(n-1)\times{7}$

$\rm\longrightarrow\:a_n=3+7n-7$

$\rm\longrightarrow\:a_n=7n-4$

Then,

According to the question,

$\rm\:61+2n=7n-4$

$\rm\longrightarrow\:61+4=7n-2n$

$\rm\longrightarrow\:65=5n$

$\rm\longrightarrow\:\cancel\dfrac{65}{5}=n$

$\rm\longrightarrow\:13=n$

$\rm\longrightarrow\:n=13$

Hence,13th term of these APs are equal.