Question

An ap consists of 3 terms whose sum is 15 and sum of the squares of the extremes is 58. find the sum of first 50 terms of an ap

Answer 1

3a=15

a= 5

given (a-d)^2+(a+d)^2=58

25+d^2-2ad+25+d^2+2ad=58

50+2d^2=58

2d^2-8=0

d^2-4=0

d=2

s50=25[10+98]

=2700

mark brainliest pls

Answer 2

The sum of first 50 terms of an ap when d = 2 is 2700

The sum of first 50 terms of an ap when d = -2 is -2200

Step-by-step explanation:

let a-d ,a,a+d  be the three terms of the AP

sum of the three terms = 15

then,

a-d+a+a+d = 15

3a = 15

a =5

sum of the square of the extremes = 58

(a-d)² - (a+d)² = 58

2(a²+d²) = 58

a²+d² = $\frac{58}{2}$

putting the value of a = 5

(5)² + d² = 29

d² = 29 - 25

d² = 4

d = $\sqrt{4}$

d = +2,-2

if d = +2

now sum of first 50 terms

case 1: n= 50 a= 5  d = +2

$S_n = \frac{n}{2} (2a+(n-1)d)$

$S_5_0= \frac{50}{2} (2(5)+(50-1)2)$

$S_5_0= 25 (10+49\times2)$

$S_5_0= 25(10+98)$

$S_5_0= 25\times 108$

$S_5_0= 2700$

case 2: n= 50 , a=5 , d= -2

$S_n = \frac{n}{2} (2a+(n-1)d)$

$S_5_0= \frac{50}{2} (2(5)+(50-1)(-2))$

$S_5_0= 25 (10+49\times(-2))$

$S_5_0= 25\times (-88)$

∞$S_5_0= - 2200$

hence , the sum of first 50 terms of an ap when d = 2 is 2700

the sum of first 50 terms of an ap when d = -2 is -2200

#Learn more:

An ap consists of 3 terms whose sum is 15 and sum of the square of extremes is 58 . Find the terms

https://brainly.in/question/5894620