Question

In the following APs,find the missing terms in the boxes

1). 5_,_,9/2
2).-4,_,_,_,_,6
3)._,38,_,_,_,-22​

Answer 1

see explanation

Explanation:

The n th term of an AP is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

(1)

Given a₁ = 5 and a₄ =
`(9)/(2)` , then

5 + 3d =
`(9)/(2)` ( subtract 5 from both sides )

3d = -
`(1)/(2)` ( divide both sides by 3 )

d = -
`(1)/(6)`

add -
`(1)/(6)` to each term

5,
`(29)/(6)`,
`(14)/(3)`,
`(9)/(2)`

(2)

Given a₁ = - 4 and a₆ = 6, then

- 4 + 5d = 6 ( add 4 to both sides )

5d = 10 ( divide both sides by 5 )

d = 2

Add 2 to each term

- 4, -2, 0, 2, 4, 6

(3)

Given a₂ = 38 and a₆ = - 22, then

a₁ + d = 38 → (1)

a₁ + 5d = - 22 → (2)

Subtract (1) from (2) term by term

4d = - 60 ( divide both sides by 4 )

d = - 15

Substitute d = - 15 into (1)

a₁ - 15 = 38 ( add 15 to both sides )

a₁ = 53

Thus

53, 38, 8, - 7, - 22