Find the missing terms :- .........., .........., 8, .........., -1

16, 10 and 2

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17, 12 and 3

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17, 12.5 and 3.5

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1, 2 and 3

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Solution

The correct option is C 17, 12.5 and 3.5
Third term, $a_{3} = 8$
Fifth term, $a_{5} = - 1$
we know that, $a_{n} = a + (n - 1) d$
$a_{3} = a + (3 - 1) d$
$a_{3} = a + 2 d$ ...... (1)
$a_{5} = a + (5 - 1) d$
$- 1 = a + 4 d$ ....... (2)
comparing equation (1) & (2)
$8 = a + 2 d$ .... (1)
$- 1 = a + 4 d$ .... (2)
(+) (-) (-)
-------------------
$a = - 2 d$
$d = - 4.5$
Put $d = - 4.5$ in equation (1)
$8 = a + 2 (- 4.5)$
$8 = a - a$
$a = 17$
$∴ a_{2} = 17 + (2 - 1) d$
$= 17 + 1 (- 4.5)$
$a_{2} = 12.5$
$a_{4} = 17 + (4 - 1) (- 4.5)$
$a_{4} = 3.5$
The missing terms are 17, 12.5 and 3.5

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