Question

An AP consists of 3 terms whose number is 15 of their squares of extreme is 58. Find the first 3 terms AP and also sum of first 50 terms of AP?

Answer 1

Step-by-step explanation:

Given An AP consists of 3 terms whose number is 15 and sum of their squares of extremes is 58. Find the first 3 terms AP and also sum of first 50 terms of AP?

• Let a – d, a, a+ d be 3 numbers in A.P
• So a – d + a + a + d = 15
• 3a = 15
• Or a = 5
• According to question sum of extremes = 58
• So (a – d)^2 + (a + d)^2 = 58
• So a^2 + d^2 – 2ad + a^2 + d^2 + 2ad
• 2(a^2 + d^2) = 58
• So a^2 + d^2 = 29
• Now 5^2 + d^2 = 29
• Or d^2 = 29 – 25
• Or d^2 = 4
• Or d = +- 2
• Therefore numbers are a – d = 5 – 2 = 3
•                                 So a + d = 5 + 2 = 7
• So the numbers are 3, 5, 7

Reference link will be

https://brainly.in/question/14765875