plete any one of the following activities :
In an A.P., the sum of three consecutive terms is 24 and their product is 312
Complete the following activity to find the terms. (The terms in AP are
iscending order)
Answers
Correct Question :
In an A.P., the sum of three consecutive terms is 24 and their product is 312.
Complete the following activity to find the terms. (The terms in A.P. are in
ascending order).
AnswEr :
Let the concecutive terms of AP be (a – d), a, and (a + d).
★ Sum of Consecutive Terms of AP :
↠ (a – d) + a + (a + d) = 24
↠ (a + a + a) + (d – d) = 24
↠ 3a = 24
- Dividing both term by 3
↠ a = 8
★ Product of Consecutive Terms of AP :
↠ (a – d) × a × (a + d) = 312
- Putting the value of a
↠ (8 – d) × 8 × (8 + d) = 312
- Dividing both term by 8
↠ (8 – d)(8 + d) = 39
- (a – b)(a + b) = (a² – b²)
↠ ((8)² – d²) = 39
↠ 64 – d² = 39
↠ 64 – 39 = d²
↠ 25 = d²
- Squaring Root Both Sides
↠ d = ± 5
━━━━━━━━━━━━━━━━━━━━━━━━
• When a = 8 and, d = 5 :
⇀ (a – d) a , (a + d) ...
⇀ (8 – 5) , 8 , (8 + 5) …
⇀ 3 , 8 , 13 …
__________________________
• When a = 8 and, d = - 5 :
⇁ (a – d) , a , (a + d) ...
⇁ (8 – (- 5)) , 8 , (8 + (- 5)) …
⇁ (8 + 5) , 8 , (8 – 5) …
⇁ 13 , 8 , 3 …
∴ The three terms of an AP in Ascending Order are 3, 8 and 13.
Answer:
in the A.p the sum of the consecutive term is 24 and their product is 312 complete the following