Complete the following patterns: a) 373, 374, 376, ?, ?, ? b) 650, 653, 659, ?, ?, ? c) 298, 303, 313, ?, ?, ? d) 642, 644, 648, ?, ?, ? e) 589, 593, 601, ?, ?, ? f) 461, 467, 479, ?, ?, ?

$$373, 374, 376, \textbf{379}, \textbf{383}, \textbf{388}$$

• $373 + 1 = 374$
• $374 + 2 = 376$
• $376 + 3 = 379$
• $379 + 4 = 383$
• $383 + 5 = 388$

$$650, 653, 659, \textbf{671}, \textbf{695}, \textbf{743}$$

• $650 + 3 = 653$
• $653 + 6 = 659$
• $659 + 12 = 671$
• $671 + 24 = 695$
• $695 + 48 = 743$

$$298, 303, 313, \textbf{333}, \textbf{373}, \textbf{453}$$

• $298 + 5 = 303$
• $303 + 10 = 313$
• $313 + 20 = 333$
• $333 + 40 = 373$
• $373 + 80 = 453$

$$642, 644, 648, \textbf{656}, \textbf{672}, \textbf{704}$$

• $642 + 2 = 644$
• $644 + 4 = 648$
• $648 + 8 = 656$
• $656 + 16 = 672$
• $672 + 32 = 704$

$$589, 593, 601, \textbf{617}, \textbf{649}, \textbf{713}$$

• $589 + 4 = 593$
• $593 + 8 = 601$
• $601 + 16 = 617$
• $617 + 32 = 649$
• $649 + 64 = 713$

$$461, 467, 479, \textbf{503}, \textbf{551}, \textbf{647}$$

• $461 + 6 = 467$
• $467 + 12 = 479$
• $479 + 24 = 503$
• $503 + 48 = 551$
• $551 + 96 = 647$

Collecting shells

This is a geometric progression where the number of shells doubles each day.
The formula for the $n$-th term of a geometric progression is $a_n = a_1 \cdot r^{n-1}$, where $a_1$ is the first term and $r$ is the common ratio.