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 2024 Slot 2The sum of the infinite series is 15(15−17)+(15)2((15)2−(17)2)+(15)3((15)3−(17)3)+….\frac{1}{5}\left(\frac{1}{5}-\frac{1}{7}\right)+\left(\frac{1}{5}\right)^{2}\left(\left(\frac{1}{5}\right)^{2}-\left(\frac{1}{7}\right)^{2}\right)+\left(\frac{1}{5}\right)^{3}\left(\left(\frac{1}{5}\right)^{3}-\left(\frac{1}{7}\right)^{3}\right)+\ldots .51(51−71)+(51)2((51)2−(71)2)+(51)3((51)3−(71)3)+….. equal toCAT 2018 Slot 2The value of the sum 7×11+11×15+15×19+⋯+95×997 \times 11 + 11 \times 15 + 15 \times 19 + \dots + 95 \times 997×11+11×15+15×19+⋯+95×99 isCAT 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