Question
In the $AP, 38, ? , ? , ? , –22,$ find the missing terms$?$
✓
Answer
Let the first terms and the common difference of the given $AP$ be a and d respectively.
$ \Rightarrow a + (2 - 1)d = 38 \because {a_n} = a + (n - 1)d$
$ \Rightarrow a + d = 38 ....... (1)$
Sixth term $= -22$
$ \Rightarrow a + (6 - 1) d = -22$
$ \Rightarrow a + 5d = -22 ......... (2)$
Solving $(1)$ and $(2),$ we get
$a = 53$
$d = -15$
Therefore,
Third term $= 53 + (3 - 1) (-15) \because {a_n} = a + (n - 1)d$
$= 53 - 30$
$= 23$
Fourth term $= 53 + (4 - 1) (-15) \because {a_n} = a + (n - 1)d$
$= 8$
Fifth $= 53 + (5 - 1) (-15) \because {a_n} = a + (n - 1)d$
$= -7$
Hence, the missing terms in the boxes are $53, 23, 8, -7$
$ \Rightarrow a + (2 - 1)d = 38 \because {a_n} = a + (n - 1)d$
$ \Rightarrow a + d = 38 ....... (1)$
Sixth term $= -22$
$ \Rightarrow a + (6 - 1) d = -22$
$ \Rightarrow a + 5d = -22 ......... (2)$
Solving $(1)$ and $(2),$ we get
$a = 53$
$d = -15$
Therefore,
Third term $= 53 + (3 - 1) (-15) \because {a_n} = a + (n - 1)d$
$= 53 - 30$
$= 23$
Fourth term $= 53 + (4 - 1) (-15) \because {a_n} = a + (n - 1)d$
$= 8$
Fifth $= 53 + (5 - 1) (-15) \because {a_n} = a + (n - 1)d$
$= -7$
Hence, the missing terms in the boxes are $53, 23, 8, -7$
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