Question

Find the AP whose 10th term is 5 and 18 term is 77.
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Answer 1

Hii There!!

Here is your answer

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Given, a10 = 5

=) a10 => a + 9d = 5 ---------1) [ since, an= a+ (n-1) d]

similarly,


=) a18 => a + 17d = 77 -------2)


Now eq. 2) - 1) we get

=) 8d = 72

=) d = 72/8 = 9

=) d= 9

Now, substituting the value of 'd' in eq 1) we get :-

=) a + 81 = 5

=) a = 5 - 81

=) a = -76

Therefore, the A.P is -76 , -67, and so on....

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Hope it helps

#DK
Dear P

Answer 2

We know that sum of n terms of an AP = a + (n - 1) * d

Given 10th term of an AP is 5.

= > a + (10 - 1) * d = 5

= > a + 9d = 5  ---- (1)


Given 18th term of an AP is 77.

= > a + (18 - 1) * d = 77

= > a + 17d = 77  ---- (2) 


On solving (1) & (2), we get

a + 9d = 5

a + 17d = 77

------------------

      -8d = -72

           d = 9


Substitute d = 9 in (1), we get

= > a + 9d = 5

= > a + 9(9) = 5

= > a + 81 = 5

= > a = 5 - 81

= > a = -76.



Therefore the AP is -76, -67.



Hope this helps!