10th std Maths part1
Answers
Answer:
sorry is not right
Step-by-step explanation:
Given :-
The sum of three consecutive terms that are in A.P is 27 and their product is 288.
To Find :-
What is the three terms.
Solution :-
Let,
\mapsto↦ First consecutive terms be a - d
\mapsto↦ Second consecutive terms be a
\mapsto↦ Third consecutive terms will be a + d
First, we have to find the sum :
\implies \sf (a - d) + a + (a + d) =\: 27⟹(a−d)+a+(a+d)=27
\implies \sf a - d + a + a + d =\: 27⟹a−d+a+a+d=27
\implies \sf a + a + a \cancel{- d} \cancel{+ d} =\: 27⟹a+a+a
−d
+d
=27
\implies \sf 3a =\: 27⟹3a=27
\implies \sf a =\: \dfrac{\cancel{27}}{\cancel{3}}⟹a=
3
27
\implies \sf\bold{\green{a =\: 9}}⟹a=9
Now, we have to find the product :
\implies \sf (a - d) \times a \times (a + d) =\: 288⟹(a−d)×a×(a+d)=288
\implies \sf 9({a}^{2} - {d}^{2}) =\: 288⟹9(a
2
−d
2
)=288
Given :
a = 9
\implies \sf 9({9}^{2} - {d}^{2}) =\: 288⟹9(9
2
−d
2
)=288
\implies \sf 9(81 - {d}^{2}) =\: 288⟹9(81−d
2
)=288
\implies \sf 729 - 9{d}^{2} =\: 288⟹729−9d
2
=288
\implies \sf - 9{d}^{2} =\: 288 - 729⟹−9d
2
=288−729
\implies \sf \cancel{-} 9{d}^{2} =\: \cancel{-} 441⟹
−
9d
2
=
−
441
\implies \sf 9{d}^{2} =\: 441⟹9d
2
=441
\implies \sf {d}^{2} =\: \dfrac{\cancel{441}}{\cancel{9}}⟹d
2
=
9
441
\implies \sf {d}^{2} =\: 49⟹d
2
=49
\implies \sf d =\: \sqrt{49}⟹d=
49
\implies \sf\bold{\pink{d =\: 7}}⟹d=7
Hence, we get :
a = 9
d = 7
Hence, the required three terms are :
\clubsuit♣ First consecutive terms :
\leadsto \sf a - d⇝a−d
\leadsto \sf 9 - 7⇝9−7
\leadsto \sf\bold{\red{2}}⇝2
\clubsuit♣ Second consecutive terms :
\leadsto \sf a⇝a
\leadsto \sf\bold{\red{9}}⇝9
\clubsuit♣ Third consecutive terms :
\leadsto \sf a + d⇝a+d
\leadsto \sf 9 + 7⇝9+7
\leadsto\sf\bold{\red{16}}⇝16
\therefore∴ The three terms are 2,9,16 or 16,9,2.