Question

The 7th term of an Ap is -1 and the 16th term is 17.FIND THE Nth TERM

Answer 1

AnsWer :

- 13 , - 11 , - 9.....

SolutioN :

Let,

• First term be a
• Common difference be d
• an = a + ( n - 1 ) d.

Case 1

• The 7th term of an Ap is - 1.

$\tt \dagger \: \: \: \: \: a_7 = - 1.$

Case 2.

$\tt \dagger \: \: \: \: \: a_{16} = 17$

Let's Find the nth terms.

$\tt \dagger \: \: \: \: \: \boxed{\tt a_n = a + (n - 1)d}$

Taking Case 1.

$\tt : \implies \tt a_7 = - 1.$

$\tt : \implies a + (7 - 1)d = - 1.$

$\tt : \implies a + 6d = - 1. \: \: \: \: \: - (1)$

Taking case 2.

$\tt : \implies a +(16 - 1)d = 17.$

$\tt : \implies a + 15d = 17. \: \: \: \: \: - (2)$

Subtraction, Equation ( 1 ) and ( 2 )

$\tt a + 15d = 17.$

$\tt a + 6d = - 1.$

________________________________

$\tt : \implies9d = 18.$

$\tt : \implies d = \dfrac{18}{9}$

$\tt : \implies d = 2.$

Now, Putting the value of d = 2. ( in Case 1 )

$\tt : \implies a + 6d = - 1.$

$\tt : \implies a + 6(2)= - 1.$

$\tt : \implies a +12 = - 1.$

$\tt : \implies a = - 1 - 12.$

$\tt : \implies a = - 13.$

$\rule{200}3$

Let find nth terms.

→ an = a + ( n - 1 )d.

• n = 1 , 2 , 3...
• a = - 13.
• d = 2.

$\tt \dagger \: \: \: \: \: a_1 = a + (n - 1)d$

$\tt : \implies a_1 = - 13 + (1- 1)2$

$\tt : \implies a_1 = - 13 +0$

$\tt : \implies a_1 = - 13.$

$\rule{200}3$

$\tt : \implies a_2 = - 13 +(2 - 1)2$

$\tt : \implies a_2 = - 13 +2$

$\tt : \implies a_2 = - 11.$

$\rule{200}3$

$\tt : \implies a_3 = - 13 +(3- 1)2$

$\tt : \implies a_3= - 13 +4$

$\tt : \implies a_3 = -9.$

Therefore, the value of nth of AP , - 13 , - 11 , - 9 .... so on.