2. The sum of three consecutive terms of an AP is 30. The sum of their squares is 3/8. Find
the terms of AP.
The sum of 7th and 11th terms of an AP is 35. The sum of its 9th and 13th term is 55.
Answers
ANSWER:-
What is the sum of n terms of an AP?
☞ The sum of n terms of AP is the sum(addition) of first n terms of the arithmetic sequence. It is equal to n divided by 2 times the sum of twice the first term – 'a' and the product of the difference between second and first term-'d' also known as common difference, and (n-1), where n is numbers of terms to be added.
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Step-by-step explanation:
a-d, a, a+d be the numbers...
Given, sum of three consecutive terms is 30. so,
a-d + a + a+d =30
3a = 30
therefore, a=10
And sum of their square is 3/8...
so, (a-d)^2 + a^2 + (a+d)^2 =3/8
a2+ d2 - 2ad + a2 + a2 + d2 + 2ad =3/8
3a^2 + 2d^2=3/8
8(3a2 + 2d2) =3
24a2+ 16d2= 3
16d2= 3-24(10)2
16d2= 3-2400
d2 =2397/16
d2 =149.8
d= sq. root of 149.8
therefore, d=12.2
then the AP is: a, a+d, a+2d,....
=10, 10+12.2, 10+(2)(12.2), ....
=10, 22.2, 34.4,...
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