MATH HELP! [Arithmetic Sequences] 10th Grade.

1. Consider the arithmetic series 2 + 5 + 8 +...
a) Find an expression for S(n), the sum of the first n terms.
b) Find the value of n for which S(n)= 1365.

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2. Ashley&Billie are swimmers training for a competition.

A) Ashley trains for 12 hrs in the first week. She decides to increase the amount of time she spends training by 2 hrs each week. Find the total number of hrs she spends training during the first 15 weeks.

B) Billie trains for 12 hours in the first week. She decides to train for 10% longer each week than the previous week.
i) Show that in the third week she trains for 14.52 hours.
ii) Find the total number of hours she spends training during the first 15 weeks.

C) In which week will the time Billie spends training first exceed 50 hrs?

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3. Arturo goes swimming every week. He swims 200 metres in the first week. Each week he swims 30 metres more than the previous week. He continues for a year. (52 weeks)

a) How far does Arturo swim in the final week?
b) How far does he swim altogether?

4. An arithmetic sequence has 5 & 13 as its first two terms respectively.
a) Write down, in terms of n, an expression for the nth term a(n).
b) Find the number of terms of the sequence which are less than 400.

CAN YOU EXPLAIN/SHOW HOW TO DO IT? I wanna learn too. Haha.
Thanks in advance!