Question

I need someone's help

Answer 1

6th term, a₆ = 12

8th term a₈ = 22

To find the common difference, d

a₈ - a₆ = 22 - 12

⇒ (a + 7d) - (a + 5d) = 10

⇒ a - a +7d - 5d = 10

⇒ 2d = 10

⇒ d = 10/2 = 5

To find the first term, a

a + 5d = 12

⇒ a + 5×5 = 12

⇒ a = 12 - 25

⇒ a = -13

2nd term, a₂ = a + d = -13 + 5 = -8

$r^{th}\ term,\ a_r=a+(r-1)d\\ \\ \Rightarrow a_r = -13+(r-1)5\\ \\ \Rightarrow a_r = -13+5r-5\\ \\ \Rightarrow \boxed{a_r = 5r-18}$

Answer 2

#AlexaRousey here!!

Let first term be a and common difference be d.

According to question ;

=) a6 = 12

=) a + (6-1)d = 12

=) a + 5d = 12 .. Eq1.

& a8 = 22

=) a + (8-1)d = 22

=) a + 7d = 22 .. Eq2.

Subtract eq1 from 2.

=) a+7d - (a+5d) = 22-12

=) 2d = 10

=) d = 10/2 = 5

Put the value of d in eq1.

=) a + 5(5) = 12

=) a + 25 = 12

=) a = 12-25 = -13

Hence a2 = a+d

= - 13 + 5

= - 8.

a(r) = a+ (r-1)d

= - 13 + (r-1)5

= 5r - 18

Hope it helps!!