The sum of the first three terms of an Arithmetic Progres...
The sum of the first three terms of an Arithmetic Progression (A.P) is 18. If the first term is 4, find their product
130
192
210
260
Correct answer is B
\(S_{n} = \frac{n}{2}(2a + (n - 1)d)\) ( for an arithmetic progression)
\(S_{3} = 18 = \frac{3}{2}(2(4) + (3 - 1) d) \)
\(18 = \frac{3}{2} (8 + 2d)\)
\(18 = 12 + 3d \implies 3d = 6\)
\(d = 2\)
\(\therefore T_{1} = 4 \implies T_{2} = 4 + 2 = 6; T_{3} = 6 + 2 = 8\)
Their product = \(4 \times 6 \times 8 = 192\)
Calculate, correct to one decimal place, the angle between 5i + 12j and -2i + 3j. ...
Given that \((\sqrt{3} - 5\sqrt{2})(\sqrt{3} + \sqrt{2}) = p + q\sqrt{6}\), find q....
Given that \(f : x \to x^{2}\) and \(g : x \to x + 3\), where \(x \in R\), find \(f o g(2)\)....
A stone is thrown vertically upward and distance, S metres after t seconds is given by S = 12t ...
If \(2\sin^{2} \theta = 1 + \cos \theta, 0° \leq \theta \leq 90°\), find the value of \(\the...
Consider the following statements: X: Benita is polite y: Benita is neat z: Benita is intel...
If the mean of 2, 5, (x + 1), (x + 2), 7 and 9 is 6, find the median. ...
Simplify \(\frac{1 + \sqrt{8}}{3 - \sqrt{2}}\)...
A body is kept at rest by three forces \(F_{1} = (10N, 030°), F_{2} = (10N, 150°)\) and \(F_...