If 5th, 8th and 11th terms of a G.P. are x, y and z respectively, then which one of the following is correct?
y² = x²z²
y² = x² + z²
y² = xz
xyz = 1

Question

If 5th, 8th and 11th terms of a G.P. are x, y and z respectively, then which one of the following is correct? 1. y2 = x2z2 2. y2 = x2 + z2 3. y2 = xz 4. xyz = 1

KnowledgeBoat · Accepted Answer

Let first term of G.P. be a and common ratio be r.

Given,

5th term = x

x = ar^{5 - 1}

x = ar⁴

8th term = y

y = ar^{8 - 1}

y = ar⁷

11th term = z

z = ar^{11 - 1}

z = ar¹⁰

Substituting value of y in L.H.S. of y² = xz

⇒ y²

⇒ (ar⁷)²

⇒ (a²r¹⁴)

Substituting value of x and z in R.H.S. of y² = xz

⇒ xz

⇒ ar⁴ × ar¹⁰

⇒ a²r¹⁴.

Since, R.H.S. = L.H.S.

Hence proved, that y² = xz.

Hence, option 3 is the correct option.

Mathematics

If 5th, 8th and 11th terms of a G.P. are x, y and z respectively, then which one of the following is correct?
y² = x²z²
y² = x² + z²
y² = xz
xyz = 1

G.P.

Answer

Related Questions

If x, y and z are in G.P., then the relation between x, y and z can be :
y = x + z
y = xz
2y = x + z
$y = \sqrt{xz}$

The product of first five terms of a G.P. with first term a and common ratio r > 1 is equal to :
$\dfrac{a(r^5 - 1)}{r - 1}$
ar⁴
a⁵r¹⁰
$\dfrac{a(r^5 - 1)}{r}$

Consider the G.P. a, ar, ar², …….., l. The kth term from the end is :
$\dfrac{l}{r^{k-1}}$
$\dfrac{l}{k}$
$\dfrac{al}{r^k}$
$\dfrac{l}{ar^{k-1}}$

If a and l are respectively the first and the last terms of a G.P. having common ratio r > 1, then the sum to n terms of the G.P. is given by :
lar^{n - 1}
ar^ln
$\dfrac{lr - a}{r - 1}$
$\dfrac{lr^n - a}{lr - 1}$

Mathematics

If 5th, 8th and 11th terms of a G.P. are x, y and z respectively, then which one of the following is correct?y2 = x2z2y2 = x2 + z2y2 = xzxyz = 1

G.P.

Answer

Related Questions

If x, y and z are in G.P., then the relation between x, y and z can be :y = x + zy = xz2y = x + zy=xzy = \sqrt{xz}y=xz​

The product of first five terms of a G.P. with first term a and common ratio r > 1 is equal to :a(r5−1)r−1\dfrac{a(r^5 - 1)}{r - 1}r−1a(r5−1)​ar4a5r10a(r5−1)r\dfrac{a(r^5 - 1)}{r}ra(r5−1)​

Consider the G.P. a, ar, ar2, …….., l. The kth term from the end is :lrk−1\dfrac{l}{r^{k-1}}rk−1l​lk\dfrac{l}{k}kl​alrk\dfrac{al}{r^k}rkal​lark−1\dfrac{l}{ar^{k-1}}ark−1l​

If a and l are respectively the first and the last terms of a G.P. having common ratio r > 1, then the sum to n terms of the G.P. is given by :larn - 1arlnlr−ar−1\dfrac{lr - a}{r - 1}r−1lr−a​lrn−alr−1\dfrac{lr^n - a}{lr - 1}lr−1lrn−a​

If 5th, 8th and 11th terms of a G.P. are x, y and z respectively, then which one of the following is correct?
y² = x²z²
y² = x² + z²
y² = xz
xyz = 1

If x, y and z are in G.P., then the relation between x, y and z can be :
y = x + z
y = xz
2y = x + z
$y = \sqrt{xz}$

The product of first five terms of a G.P. with first term a and common ratio r > 1 is equal to :
$\dfrac{a(r^5 - 1)}{r - 1}$
ar⁴
a⁵r¹⁰
$\dfrac{a(r^5 - 1)}{r}$

Consider the G.P. a, ar, ar², …….., l. The kth term from the end is :
$\dfrac{l}{r^{k-1}}$
$\dfrac{l}{k}$
$\dfrac{al}{r^k}$
$\dfrac{l}{ar^{k-1}}$

If a and l are respectively the first and the last terms of a G.P. having common ratio r > 1, then the sum to n terms of the G.P. is given by :
lar^{n - 1}
ar^ln
$\dfrac{lr - a}{r - 1}$
$\dfrac{lr^n - a}{lr - 1}$