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8. Sequences and Series
easy
If the sum of three consecutive terms of an $A.P.$ is $51$ and the product of last and first term is $273$, then the numbers are
A
$21, 17, 13$
B
$20, 16, 12$
C
$22, 18, 14$
D
$24, 20, 16$
Solution
(a) Let consecutive terms of an $A.P.$ are $a – d,\;a,\;a + d$.
Under given condition, $(a – d) + a + (a + d) = 51$
$ \Rightarrow $ $a = 17$ and $(a – d)(a + d) = 273$
$ \Rightarrow $ ${a^2} – {d^2} = 273$
$ \Rightarrow $ $ – {d^2} = 273 – 289$
$ \Rightarrow $ $d = 4$
Hence consecutive terms are $13, 17, 21.$
Trick : Both conditions are satisfied by $(a)$ $i.e.$ $21, 17, 13.$
Standard 11
Mathematics
