Question

How many non square no.. lie between 90^2. And. 91^2

Answer 1

★ Given :

A.P : (90)² ........ (91)²

A P = 8100, 8101 ....…. 8281.

First term (a) = 8101

Common Difference (D) = 1

Last term (An) = 8280

$\rule{200}{1}$

★ Solution :

In the question we will not use a as 8100 and An as 8281 because we have to find non-zero number between 8100 and 8281.

We know that,

$\Large{\implies{\boxed{\boxed{\sf{A_n = a + (n - 1)d}}}}}$

★ Putting Values ★

$\sf{\dashrightarrow 8280 = 8100 + (n - 1)1} \\ \\ \sf{\dashrightarrow 8280 - 8100 = n - 1} \\ \\ \sf{\dashrightarrow 180 = n - 1} \\ \\ \sf{\dashrightarrow n = 180 + 1} \\ \\ \sf{\dashrightarrow n = 181}$

$\Large{\implies{\boxed{\boxed{\sf{n = 181}}}}}$

Answer 2

★ Given :

• A.P : (90)² ........ (91)²

• A P = 8100, 8101 ....…. 8281.

• First term (a) = 8101

• Common Difference (D) = 1

• Last term (An) = 8280

★ Solution :

In the question we will not use a as 8100 and An as 8281 because we have to find non-zero number between 8100 and 8281.

We know that,

$\large\boxed{ \boxed{ \bf \purple{A_n = a + (n - 1)d}}}$

★ Putting Values ★

$\sf{\dashrightarrow 8280 = 8100 + (n - 1)1} \\ \\ \sf{\dashrightarrow 8280 - 8100 = n - 1} \\ \\ \sf{\dashrightarrow 180 = n - 1} \\ \\ \sf{\dashrightarrow n = 180 + 1} \\ \\ \sf{\dashrightarrow n = 181}\\ \\</p><p>\Large{\implies{\boxed{\boxed{\sf{ \green{n = 181}}}}}}$