1(xv)
Assertion (A): The 9th term of a Geometric Progression (G.P.) 6, −12, 24, −48, ... is a positive term.
Reason (R): The value of (−2)8 is always positive.
- (a)(A) is true and (R) is false.
- (b)(A) is false and (R) is true.
- (c)Both (A) and (R) are true and (R) is the correct explanation of (A).
- (d)Both (A) and (R) are true but (R) is not the correct explanation of (A).
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Given,
6, −12, 24, −48... is a G.P.
a = 6
r = $\frac{-12}{6}$ = -2
By formula,
an = arn - 1
For 9th term,
⇒ a9 = (6).(-2)9 - 1
= 6.(-2)8
= 6.(256)
= 1536 > 0.
∴ Assertion (A) is true.
(-2)8
Any negative number raised to an even power is always positive.
∴ Reason (R) is true.
Thus, both (A) and (R) are true and (R) is the correct explanation of (A).
Hence, option 3 is the correct option.