Question

Find the 20th term of an ap whose 3rd term is 7 and the 7th term exceeds thre times the 3rd term by2. Also find its nth term

Answer 1

$\mathfrak{\huge{Answer:}}$

Given is that : 3rd term of the AP = 7

7th term = 23

We know that the nth term of an AP = a + ( n - 1 )d

Where,

a = first term of the AP

d = common difference

For the 3rd term, using the formula :

a + ( n - 1 )d = $\sf{a_{n}}$

The values will be =》 a + ( 3 - 1 )d = 7

=》 a + 2d = 7

=》 a = 7 - 2d

For the 7th term, firstly, we need to take out the value =》 3(7) + 2 = 23

For the 7th term =》 a + ( 7 - 1 )d = 23

=》 a + 6d = 23

=》 a = 23 - 6d

a = a ( the first term will always be the same )

=》 7 - 2d = 23 - 6d

=》 4d = 16

=》 d = 4

a = 7 - 8

a = ( -1 )

Now, we've got the real values of a and d. The 20th term will be :

( -1 ) + ( 20 - 1 )4

=》 ( -1 ) + 76

=》 $\boxed{\mathfrak{20th\:term = 75}}$

nth term of the AP = a + ( n - 1 )d

Put the values of a and d :-

=》 ( -1 ) + ( n - 1 )4

=》 4n - 4 - 1

=》 $\boxed{\mathfrak{nth\:term=4n - 5}}$

Answer 2

Question :

Find the 20th term of an ap whose 3rd term is 7 and the 7th term exceeds three times the 3rd term by 2. Also find its nth term.

Answer :

20th term = 75

nth term = 4n - 5

Step by step explanation :

Refer the attachments for the answer.

[ In an A.P, the first term is denoted by a and the common difference is denoted by d ]

To find the nth term of an A.P, we use the formula :

Tn = a + ( n - 1 ) d

Hence,

We get the values as :

a = -1

d = 4

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Final answer :

20th term = 75

nth term = 4n - 5