Question

विावध
समान्तर श्रेढी में पाँच संख्याओं का योग 25 और उनके वर्गों का योग 135 है, संत्र
[उत्तर : 3,4,5,617​

Answer 1

Answer:

Step-by-step explanation:

terms of AP are 3, 4, 5, 6 and 7

Step-by-step explanation:

Let a be the first term of the A.P and d be the common difference.

then,  the 5 terms be (a-2d ), (a-d) , a , (a+d) and (a+2d)

then according to question,

Sum of terms is 25.

⇒ (a-2d ) + (a-d) + a + (a+d) + (a+2d) = 25

⇒ 5a = 25

⇒ a= 5

Also given , sum of squares of terms of AP is 135

that is  

Put a = 5 and evaluate we get,

Solve for d, we get,

Thus, terms are

Case 1) when a = 5 and d= 1

(a-2d ) = 5-2 = 3

(a-d) = 5-1 = 4

a = 5

(a+d) = 5+1 = 6

and (a+2d) = 5 +2 = 7

Case 2) when a = 5 and d= -1

(a-2d ) = 5+2 = 7

(a-d) = 5+1 = 6

a = 5

(a+d) = 5-1 = 4

and (a+2d) = 5 - 2 = 3

Thus, terms of AP are 3, 4, 5, 6 and 7