Progression (Sequence and Series)Easy
Question
If for an AP a1, a2, a3.....,an,...... ......a1 + a3 + a5 = -12 and a1 a2 a3 = 8then the value of a2 + a4 + a6 equals :-
Options
A.-12
B.-16
C.-18
D.-21
Solution
Let the first 5 terms of AP are a - 2d, a - d, a, a + d, a + 2d
Now a1 + a3 + a5 = -12
⇒ 3a = - 12 ⇒ a = - 4
Also, a1 . a2 . a3 = 8
⇒ (a - 2d) (a - d) a = 8
(-4 - 2d) (-4 -d) (-4) = 8 ⇒ d = - 3
Hence the AP is 2, –1, -4, -7, -10, -13,...
Hence a2 + a4 + a6 = - 21
Now a1 + a3 + a5 = -12
⇒ 3a = - 12 ⇒ a = - 4
Also, a1 . a2 . a3 = 8
⇒ (a - 2d) (a - d) a = 8
(-4 - 2d) (-4 -d) (-4) = 8 ⇒ d = - 3
Hence the AP is 2, –1, -4, -7, -10, -13,...
Hence a2 + a4 + a6 = - 21
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