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Question
In the following APs, find the missing term in the box:
`5, square, square, 9 1/2`
Solution
`5, bb(6 1/2, 8), 9 1/2`
Explanation:
For this A.P.,
a = 5 and
a4 = `9 1/2`
We know that, an = a + (n − 1) d
⇒ `9 1/2 = 5 + (4 - 1) ("d")`
⇒ `9 1/2 = 5 + 3"d"`
⇒ `3d = 9 1/2 - 5`
= `4 1/2`
⇒ `"d" = 13 × 4 1/2`
= `1 1/2`
⇒ `"a"_2 = 5 + 1 1/2`
= `6 1/2`
a3 = 5 + 2 × `1 1/2`
= 5 + 3
= 8
Therefore, the missing terms are `6 1/2` and 8 respectively.
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