CATAlgebra > Medium(1003)215−3(1003)2^{15} - 3(1003)215−3(997)214+3(997)2^{14}+ 3(997)214+3(1003)15+6(1003)^{15}+ 6(1003)15+6(997)15−3(997)^{15}-3(997)15−3✅ Correct Option: 1Related questions:CAT 2023 Slot 3The value of 1+(1+13)14+(1+13+19)116+(1+13+19+127)164+……1+\left(1+\frac{1}{3}\right) \frac{1}{4}+\left(1+\frac{1}{3}+\frac{1}{9}\right) \frac{1}{16}+\left(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}\right) \frac{1}{64}+\ldots \ldots1+(1+31)41+(1+31+91)161+(1+31+91+271)641+……, isCAT 2021 Slot 2For a sequence of real numbers x1,x2,......xnx_1, x_2, ...... x_nx1,x2,......xn, if x1−x2+x3−....+(−1)n+1xn=n2+2nx_1 - x_2 + x_3 - .... + (-1)^{n + 1} x_n = n^2 + 2nx1−x2+x3−....+(−1)n+1xn=n2+2n for all natural numbers n, then the sum x49+x50x_{49} + x_{50}x49+x50 equalsCAT 2017 Slot 2Let a1,a2,a3,a4,a5a_1, a_2, a_3, a_4, a_5a1,a2,a3,a4,a5 be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with 2a32a_32a3. If the sum of the numbers in the new sequence is 450450450, then a5a_5a5 is