Question

Assertion (A): The 9^th 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.

पर्याय

• (A) is true and (R) is false.

• (A) is false and (R) is true.

• Both (A) and (R) are true and (R) is the correct explanation of (A).

• Both (A) and (R) are true but (R) is not the correct explanation of (A).

Answer 1

Both (A) and (R) are true and (R) is the correct explanation of (A).

Explanation:

Given: 6, −12, 24, −48... is a G.P.

a = 6

r = `−12/6`

= −2

By formula,

a_n = ar^{n − 1}

For 9^th 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).