Ineed with these 3 questions asap. give me a step by step explanation.
even just answering one or two out of the 3 questions will plenty
1. determine the value of the first term in the finite arithmetic series with 14 terms, a common difference of 6 and a sum of 574
2. a training program requires a pilot to fly circuits of an airfield. each day, the pilot flies three more
circuits than the previous day. on the fifth day, the pilot flew 14 circuits. how many circuits did the
pilot fly
a. on the first day?
b. in total by the end of the fifth day?
3. determine the 20th term of the sequence 32768, 16384,8192,

1) first term = 2

Step-by-step explanation:

1)  n =14 ;   d = 6 ;  Sum = 574

    Sum =n/2 * (2a + (n-1)d)

     574 = 14/2 * (2a + (14-1) * 6)

     574   = 7 * (2a + 13 * 6)

  574   = 7 * (2a +  78)

   574/ 7 = 2a + 78

     82    = 2a + 78

 82 - 78 = 2a

   4 = 2a

 a = 4/2

a =2

2) No.of circuits on first day = 14 - 12  = 2 circuits

Total by the end of fifth day  = 2 + 5 +8 +11 +14 = 40

3) n = 20 ;   a = 32768

  r = term 2  / term 1 = 16384 / 32768 = 1/2

 nth term = ar^(n-1)

20th term = 32768 * (1/2)^19

                 = 32768 * (1/ 524288)

                 = 32768 / 524288

                  = 1/16

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step-by-step explanation:

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