Question

3 no are in sequence there + is 48 and production of 1 and three trem to is 175. answer ​

Answer 1

Answer:

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: Correct Question :- \: \star}}}}}$

Three numbers are in AP there sum is 48 and product of 1st and 3rd term is 175. find the number.

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

$\large{\underline{\boxed{\bf (7,16,25) \: or \: (25,16,7)}}}$

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

Let the required numbers be (a - d), a and (a + d).

It is given that ;

Sum of numbers is 21.

⇒ a - d + a + a + d = 21

⇒ 3a = 48

⇒ a = $\sf \dfrac{48}{3}$

⇒ a = 16

Also, the product of first and third term is 175.

⇒ (a - d) * (a + d) = 175

⇒ (a² - d²) = 175

⇒ (16² - d²) = 175

⇒ 256 - d² = 175

⇒ d² = 256 - 175

⇒ d² = 81

⇒ d = ± √81

⇒ d = ± 9

Thus, a = 16 and d = ± 9.

The required numbers are;

(a - d) = (16 - 9) = 7

a = 16

(a + d) = 16 + 9 = 25

Or, the other possibility can be -

(a - d) = 16 + 9 = 25

a = 16

(a + d) = 16 - 9 = 11

$\huge\bold\star\green{Hence}\star$

The required numbers in an AP are (7, 16, 25) or (25, 16, 7).