Question

Fill in the blanks in the following table, given that a is the first term, d the common difference and 
$a_{n}$
the nth term of the AP:

Answer 1

$\huge \bf \pink{Hey \: there !! }$


(i) $a_1$ = 7 ; d = 3 ; n = 8 .

To find :- $a_n$ .


Since, nth term is given by :-

°•° $a_n$ = $a_1$ + ( n - 1 )d .

= 7 + ( 8 - 1 ) 3 .

= 7 + 21 .

= 28 .


(ii) $a_1$ = -18 ; n = 10 ; $a_n$ = 0.

To find :- d .


Since, nth term is given by :-

°•° $a_n$ = $a_1$ + ( n - 1 )d .

==> 0 = -18 + ( 10 - 1 ) d .

==> 18 = 9d.

==> d = 18/9 .

•°• d = 2 .


(iii) $a_n$ = -5 ; d = -3 ; n = 18 .

To find :- $a_1$ .


Since, nth term is given by :-

°•° $a_n$ = $a_1$ + ( n - 1 )d .

==> -5 = a + ( 18 - 1 ) -3 .

==> -5 = a - 51 .

==> a = 51 - 5 .

•°• $a_1$ = 46 .



(iv) $a_1$ = -18.9 ; d = 2.5 ; $a_n$ = 3.6 .

To find :- n .


Since, nth term is given by :-

°•° $a_n$ = $a_1$ + ( n - 1 )d .

==> 3.6 = -18.9 + ( n - 1 ) 2.5 .

==> 3.6 + 18.9 = 2.5n - 2.5 .

==> 22.5 + 2.5 = 2.5n .

==> n = 25/2.5

•°• n = 10 .


(v) $a_1$ = 3.5 ; d = 0 ; n = 105 .

To find :- $a_n$ .


Since, nth term is given by :-

°•° $a_n$ = $a_1$ + ( n - 1 )d .

= 3.5 + ( 105 - 1 ) 0 .

= 3.5 + 0 .

= 3.5 .



✔✔ Hence, it is solved ✅✅.



THANKS



#BeBrainly.

Answer 2

$\huge \bf \red{answer}$

$\bf{step \: by \: step \: explanation}$

(i) Given-

a1​ = 7
d = 3
n = 8 .

To find -
an​ =?

an​ = a1​ + ( n - 1 )d .

=>7 + ( 8 - 1 ) 3 .

=> 7 + 21 .

=> 28 .

(ii) Given-

a1​ = -18
n = 10
an​ = 0.

To find -

d=?

an​ = a1​ + ( n - 1 )d .

=>0 = -18 + ( 10 - 1 ) d .

=> 18 = 9d.

=> d = 18/9 .

d = 2 .

(iii) Given -

an​ = -5

d = -3

n = 18 .

To find =

 a1​ =?

an​ = a1​ + ( n - 1 )d

=> -5 = a + ( 18 - 1 ) -3 .

=> -5 = a - 51 .

=> a = 51 - 5 .

 a1​ = 46 .

(iv) Given-

a1​ = -18.9

d = 2.5

 an​ = 3.6 .

To find -

n=?

an​ = a1​ + ( n - 1 )d .

=> 3.6 = -18.9 + ( n - 1 ) 2.5 .

=> 3.6 + 18.9 = 2.5n - 2.5 .

=> 22.5 + 2.5 = 2.5n .

=> n = 25/2.5 

n = 10 .

(v) Given -

a1​ = 3.5
d = 0

n = 105 .

To find -

an​ =?

an​ =a1​ + ( n - 1 )d .

=> 3.5 + ( 105 - 1 ) 0 .

=> 3.5 + 0 .

= >3.5 .

$\huge{ \mathfrak{ \purple{thanks}}}$