Question

Determine 2nd term and rth term of a.p.whose 6 th term is 12 and 8 th term is 22​

Answer 1

see explanation

Explanation:

The n th term of an arithmetic progression is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given
`a_(6)` = 12 and
`a_(8)` = 22, then

a₁ + 5d = 12 → (1)

a₁ + 7d = 22 → (2)

Subtract (1) from (2) term by term to eliminate a₁

2d = 10 ( divide both sides by 2 )

d = 5

Substitute d = 5 into (1) to find a₁

a₁ + 5(5) = 12

a₁ + 25 = 12 ( subtract 25 from both sides )

a₁ = - 13

Thus

`a_(2)` = - 13 + 5 = - 8

`a_(n)` = - 13 + 5(n - 1) = - 13 + 5n - 5 = 5n - 18 ← n th term