Sum of three consecutive terms which are in AP is 27, and the sum of their square is 293. Find the terms.
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1
Answer:
apply formula sn = n/2(2n+1)
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Question:-
Sum of three consecutive terms which are in AP is 27, and the sum of their square is 293. Find the terms.
Answer :-
Let the consecutive three terms in A.P series be a-m,a,a+m.......Now as per question a-m+a+a+m=27,
or,3a=27,or,a=9.Again as per question
(a-m)^2+a^2+(a+m)^2=293,
or, a^2-2am+m^2+a^2+a^2+2am+m^2=293
or,3a^2+2m^2=293
or,3×9^2+2m^2=293
or,243+2m^2=293
or,2m^2=293-243=50
or,m^2=25
or,m=5
So,a-m=9+5=14or9-5=4
a=9
a+m=9-5=4or9+5=14
The three consecutive terms in the A.P is either,14,9,4...or 4,9,14...
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