Question

Which term of the following two arithmetic progressions is the same? Also find this
term?
(a) 13, 19, 25… (b) 69, 68, 67…

Answer 1

Answer:

Step-by-step explanation:

chinKrMbMaths AryaBhatta

Hey there !!

Let the nth terms of the given progressions be  and  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

 = a + ( n - 1 )d.

=>   = 13 + ( n - 1 ) × 6.

=>   = 13 + 6n - 6.

=>  = 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

 = A + ( n - 1 )D.

=> = 69 + ( n - 1 ) × (-1).

=>  = 69 - n + 1.

=>  = 70 - n..........(2).

▶ Now,

A/Q,

=>  =  .

=> 6n + 7 = 70 - n.

=> 6n + n = 70 - 7.

=> 7n = 63.

=> n = 

✔✔ Hence, it is solved ✅✅.

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