Question

For what value of n are the nth term of the following two ap are same 13,19,25 and 69,68,67

Answer 1

Hey there !!

Let the nth terms of the given progressions be $t \tiny{n}$ and  $T \tiny{n}$ respectively.

▶ The first AP is 13, 19, 25...... .

Let its first term be a and common difference be d. Then,

=> a = 13 and D = ( 19 - 13 ) = 6.

So, its nth term is given by

$t \tiny{n}$ = a + ( n - 1 )d.

=> $t \tiny{n}$  = 13 + ( n - 1 ) × 6.

=>  $t \tiny{n}$ = 13 + 6n - 6.

=> $t \tiny{n}$ = 6n + 7........(1).

▶ The second AP is 69, 68, 67..... .

Let its first term be A and common difference be D. Then,

=> A = 69 and D = ( 68 - 69 ) = -1.

So , its nth term is given by

$T \tiny{n}$ = A + ( n - 1 )D.

=> $T \tiny{n}$ = 69 + ( n - 1 ) × (-1).

=> $T \tiny{n}$ = 69 - n + 1.

=> $T \tiny{n}$ = 70 - n..........(2).

▶ Now,

A/Q,

=> $t \tiny{n}$ = $T \tiny{n}$ .

=> 6n + 7 = 70 - n.

=> 6n + n = 70 - 7.

=> 7n = 63.

=> n = $\frac{63}{7} .$

$\huge \boxed{ \boxed{ \bf => n = 9. }}$

✔✔ Hence, it is solved ✅✅.

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$\huge \boxed{ \mathbb{THANKS}}$ 


$\huge \bf{ \#BeBrainly. }$

Answer 2

HEY THERE!!

Let to First Arithmetic Progression tn and Tn Is second Arithmetic Progression (AP):-

First Arithmetic Progression:- 13,19,25......

Here,

a=13

d=19-13

  = 6

According to the Formula of Arithmetic Progression:- Tn=a+(n-1)d

Now, Substitute the value of first term and CommOn Difference on  Given Arithmetic Progression;-

=> Tn=a+(n-1)d

=> Tn=13+(n-1)6

=> Tn=13+6n-6

=> Tn=7+6n

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Second Arithmetic Progression:- 69,68,67.....

Here,

a=69

d=68-69

  = -1

According to the Formula of Arithmetic Progression:- Tn=a+(n-1)d

Now, Substitute the value of first term and CommOn Difference on  Given Arithmetic Progression;-

tn=a+(n-1)d

=> tn=69+(n-1)-1

=> tn=69-n+

=> tn=69+1-n

=> tn=70-n

Considering on Question;-

Both Arithmetic Progression( AP) are in same terms:-

Then,

Tn=tn

=> 7+6n=70-n

=> 7-70=-n-6n

=> -63=-7n

=> 63=7n

=> n=63/7

=> n= 9

Hence, For value of n(9) are the nth term of the following two ap are same 13,19,25 and 69,68,67

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