Question

Please answer the questions ​

Answer 1

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

h7th term = 23

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

tWhere,

ia = first term of the AP

yd = common difference

aFor the 3rd term, using the formula :

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

20thterm=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}}

nthterm=4n−5

Jhzhzg