The sum of first three terms of an AP is 45 and the sum of their squares is 693.If common difference is positive,then its fourth term is
1.27
2.18
3.21
4.24
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heya..!!!!
let the three terms be (a-d) , a , (a+d)
a-d+a+a+d =45
=> 3a = 45
=> a = 15 --- [1]
[a-d]² + a² + [a+d]² = 693
=> a² + d² - 2ad + a² + a² + d² +2ad = 693
=> 3a² + 2d²= 693 ---[2]
=> 3 [15]² + 2d² =693
=> 3 [225] +2d² = 693
=> 675 + 2d² =693
=> 2d² = 693 -675
=> 2d² = 18
=> d² = 18 /2 = 9
d = 3
a = 15 AND d= 3
(15 - 3) = 12
a = 15
(15 + 3) = 18
(12,15,18,21)
hence 4th Term = 21
let the three terms be (a-d) , a , (a+d)
a-d+a+a+d =45
=> 3a = 45
=> a = 15 --- [1]
[a-d]² + a² + [a+d]² = 693
=> a² + d² - 2ad + a² + a² + d² +2ad = 693
=> 3a² + 2d²= 693 ---[2]
=> 3 [15]² + 2d² =693
=> 3 [225] +2d² = 693
=> 675 + 2d² =693
=> 2d² = 693 -675
=> 2d² = 18
=> d² = 18 /2 = 9
d = 3
a = 15 AND d= 3
(15 - 3) = 12
a = 15
(15 + 3) = 18
(12,15,18,21)
hence 4th Term = 21
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