Sequences

The 4th term of an arithmetic sequence is 15 and the common difference is 6.

Find the sum of the first 25 terms of the arithmetic sequence: 7, 12, 17, 22, ...

Explain why the sequence 1, 2, 4, 7, 11, ... is not an arithmetic sequence.

Given the sequence 4, 9, 16, 25, 36, ..., write a formula for the nth term.

In the sequence 6, 12, 18, 24, ..., what is the common difference? Write the answer.

In a science experiment, Marta adds chemicals to a solution following this sequence: she adds 2 ml on the first day, 5 ml on the second day, 8 ml on the third day, and so on, increasing the amount by 3 ml each day.

On which day will she add exactly 44 ml to the solution?

The first term of an arithmetic sequence is 12. The common difference is 7. Calculate the sum of the first 30 terms of this sequence.

Sophie decides to save money for a holiday by following a plan: she saves $15 in the first week and then increases how much she saves by $4 each week. She needs to save at least $350. Explain how she can work out the minimum number of weeks needed to reach her goal. Show your reasoning clearly.