Question

d) 1+6+11+16+...+146
e) (-25)+(-20)+(-15)+(-10)+...+60
va rog frumoas sa ma ajutați
Mulțumesc!​

Answer 1

$d) \: 1 + 6 + 11 + ... + 146 \\ = 1 + 1 + 5 + 1 + 10 + ... + 1 + 145 \\ = 1 + 1 + 1 + ... + 1 + 5 + 10 + ... + 145 \\ = 30 \cdot 1 + 5(1 + 2 + 3 + ... + 29) \\ = 30 + 5 \cdot \tfrac{29\cdot30}{2} \\ = 3 + 5\cdot29\cdot15 \\ = 30 + 2175 \\ = 2205 \\ \\ e) \: \: - 25 - 20 - 15 - ... + 55 + 60 \\ = - 5(5 + 4 + ... + 1) + 5(1 + 2 + ... + 14) \\ = - 5\cdot \tfrac{5\cdot6}{2} + 5\cdot \tfrac{14\cdot15}{2} \\ = - 5\cdot5\cdot3 + 5\cdot7\cdot15 \\ = - 75 + 525 \\ = 450$