For a G.P., its fourth term = x, seventh term = y and tenth term = z. Assertion (A): x, y and z are in G.P. Reason (R): y2 = (ar6)² = ar³ × ar⁹ = xz. 1. A is true, R is false. 2. A is false, R is true. 3. Both A and R are true and R is correct reason for A. 4. Both A and R are true and R is incorrect reason for A.

Let first term of the G.P. be a and common ratio be r. By formula : ⇒ Tn = a.rn - 1 Given, fourth term = x, seventh term = y and tenth term = z ⇒ a4 = x, a7 = y and a10 = z ⇒ ar4 - 1 = x, ar7 - 1 = y and ar10 - 1 = z ⇒ ar3 = x, ar6 = y and ar9 = z If x, y and z are in G.P., then the ratio between the consecutive terms will be equal. Ratio between y and x : Ratio between z and y : Since, the ratio between the consecutive terms are equal. Thus, x, y and z are in G.P. ∴ Assertion (A) is true. ⇒ y2 = (ar6)2 ⇒ y2 = ar12 ⇒ y2 = ar3 × ar9 ⇒ y2 = xz. ∴ Reason (R) is true. Hence, option 3 is the correct option.

Mathematics

For a G.P., its fourth term = x, seventh term = y and tenth term = z.
Assertion (A): x, y and z are in G.P.
Reason (R): y² = (ar⁶)² = ar³ × ar⁹ = xz.
A is true, R is false.
A is false, R is true.
Both A and R are true and R is correct reason for A.
Both A and R are true and R is incorrect reason for A.

G.P.

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Mathematics

For a G.P., its fourth term = x, seventh term = y and tenth term = z.Assertion (A): x, y and z are in G.P.Reason (R): y2 = (ar6)2 = ar3 × ar9 = xz.A is true, R is false.A is false, R is true.Both A and R are true and R is correct reason for A.Both A and R are true and R is incorrect reason for A.

G.P.

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