JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(a_1 , a_2, a_3, .... , a_n\), be in \(A.P\). If \(a_3 + a_7 + a_{11} + a_{15} = 72\) , then the sum of its first \(17\) terms is equal to
- A \(306\)
- B \(204\)
- C \(153\)
- D \(612\)
Answer & Solution
Correct Answer
(A) \(306\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{l} {a_3} + {a_7} + {a_{11}} + {a_{15}} = 72\\ \left( {{a_3} + {a_{15}}} \right) + \left( {{a_7} + {a_{11}}} \right) = 72\\ {a_3} + {a_{15}} + {a_7} + {a_{11}} = \left( {{a_1} + {a_{17}}} \right) \end{array}\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The area of the region \(\{(x, y) : 0 \leq y \leq 6 - x, y^2 \geq 4x - 3, x \geq 0\}\) is:JEE Mains 2026 Medium
- Let \(S\) be the set of all triangle in the \(xy -\) plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in \(S\) has area \(50\) sq. units, then the number of elements in the set \(S\) isJEE Mains 2019 Hard
- Let \(A=\left[\begin{array}{l}a_{1} \\ a_{2}\end{array}\right]\) and \(B=\left[\begin{array}{l}b_{1} \\ b_{2}\end{array}\right]\) be two \(2 \times 1\) matrices with real entries such that \(A = XB,\) where \(X=\frac{1}{\sqrt{3}}\left[\begin{array}{cc}1 & -1 \\ 1 & k\end{array}\right],\) and \(k \in R\). If \(a _{1}^{2}+ a _{2}^{2}=\frac{2}{3}\left( b _{1}^{2}+ b _{2}^{2}\right)\) and \(\left( k ^{2}+1\right) b _{2}^{2} \neq-2 b _{1} b _{2}\) then the value of \(k\) is ....... .JEE Mains 2021 Hard
- The total number of \(3-digit\) numbers, whose sum of digits is \(10,\) isJEE Mains 2020 Hard
- If P is a point on the circle \( x^{2}+y^{2}=4 \), Q is a point on the straight line \( 5x+y+2=0 \) and \( x-y+1=0 \) is the perpendicular bisector of PQ, then 13 times the sum of abscissa of all such point P is ........... .JEE Mains 2026 Hard
- Let \(f(x)=x^{2025}-x^{2000}, x\in[0,1]\)and the minimum value of the function \(f(x)\) in the interval [0, 1] be \((80)^{80}(n)^{-81}\). Then n is equal toJEE Mains 2026 Hard
More PYQs from JEE Mains
- If the tangent at a point \(P\) on the parabola \(y ^2=3 x\) is parallel to the line \(x+2 y=1\) and the tangents at the points \(Q\) and \(R\) on the ellipse \(\frac{x^2}{4}+\frac{y^2}{1}=1\) are perpendicular to the line \(x-y=2\), then the area of the triangle \(PQR\) is:JEE Mains 2023 Hard
- If \(A = \left[ {\begin{array}{*{20}{c}}2&{ - 3}\\{ - 4}&1\end{array}} \right],\) then \(adj\;\left( {3{A^2} + 12A} \right) = \) . . . .JEE Mains 2017 Medium
- Let \(\mathrm{f}(\mathrm{x})\) be a polynomial of degree \(5\) such that \(\mathrm{x}=\pm 1\) are its critical points. \(\mathop {\lim }\limits_{x \to 0} \left(2+\frac{f(x)}{x^{3}}\right)=4,\) then which one of the following is not true?JEE Mains 2020 Hard
- The locus of the foot of perpendicular drawn from the centre of the ellipse \({x^2} + 3{y^2} = 6\) on any tangent to it isJEE Mains 2014 Hard
- Let \(A =\left[\begin{array}{ll} a & b \\ c & d \end{array}\right]\) and \(B =\left[\begin{array}{l}\alpha \\ \beta\end{array}\right] \neq\left[\begin{array}{l}0 \\ 0\end{array}\right]\) such that
\(AB = B\) and \(a + d =2021,\) then the value of \(ad - bc\) is equal to ...... .JEE Mains 2021 Medium - If \(1+\left(1-2^{2} \cdot 1\right)+\left(1-4^{2} \cdot 3\right)+\left(1-6^{2} \cdot 5\right)+\ldots \ldots+\left(1-20^{2} \cdot 19\right)\) \(=\alpha-220 \beta,\) then an ordered pair \((\alpha, \beta)\) is equal toJEE Mains 2020 Medium