Question

The sum of 5th and 9th terms of an AP is 72 and the sum of the 7 th and 12 th term is 97 . Find the AP.

Answer 1

Hey Mate ✌

Here's your answer friend,

Given : Sum of 5th and 9th teems of an arithmetic progression is 72.

and Sun of 7th and 12th terms of the Arithmetic progression is 97.

==> Let a be the first term, d be the common difference, n be the number of terms and nth term be an.

==> 5th term : a5 = a + 4d

==> ninth term : a9 = a + 8d

==> 7th term : a7 = a + 6d

==> 12th term : a12 = a + 11d

Now according to the question,

Case I : a5 + a9 = 72

===> (a + 4d) + (a + 8d) = 72

==> 2a + 12d = 72

Now Case II : a7 + a12 = 97

==> (a + 6d) + (a + 11d) = 97

==> 2a + 17d = 97..................(1)

Now let us multiply case I by (-1)

we get,

(-2a) - 12d = -72

Now by elimination method in eq(2) and eq(1) we get,

-2a - 12d = -72

2a + 17d = 97

==> 5d = 25

==> d = 5

and now by substituting d = 5 in eq (1)

we get,

2a + 17d = 97

==> 2a + 17(5) = 97

==> 2a + 85 = 97

2a = 97 - 85

==> 2a = 12

==> a = 6

Therefore,

The required Arithmetic progression is

a, a + d, a + 2d..... an

==> 6, 6 + 5, 6 + 2(5).........6n

==> 6, 11, 16............an.

⭐Hope it helps you ^_^⭐

Answer 2

Helll friend

Good evening

Your answer is given in the attachment

I hope it will help you

Thanks

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