Answer to Question #258323 in Math for Bura

Question

Find the 100th partial sum of 2+10+8+14+14+18

Answer 1

$$2+10+8+14+14+18+...$$

$$=(2+8+14+...)+(10+14+18+...)$$

Arithmetic progression $2, 8, 14, ...$

$$a=2, d=8-2=6$$

$$S_{50}=\dfrac{2(2)+6(50-1)}{2}\cdot50=7450$$

Arithmetic progression $10, 14, 18, ...$

$$a=10, d=14-10=4$$

$$S_{50}=\dfrac{2(10)+4(50-1)}{2}\cdot50=5400$$

The 100th partial sum is

$$7450+5400=12850$$

Or

$$2+10+8+14+14+18+...$$

$$=12+22+32+...$$

Arithmetic progression $10, 14, 18, ...$

$$a=12, d=22-12=10$$

$$S_{50}=\dfrac{2(12)+10(50-1)}{2}\cdot50=12850$$

The 100th partial sum is $12850.$