Question

Please answer quickly! Several questions from Algebra 2, on a unit about Sequences and Series, most of these have to do with Arithmetic and Geometric Series-screenshots of the questions are linked below. It would be great if you could include the question # and the answer in the answer section, and then explain it below. Thank you in advance!

Answer 1

The sum of the geometric series is 2199; option E.

• The 36th term of the arithmetic series is -60.5 option C
• The sum of the arithmetic series is 2547; option E
• The missing geometric sequence are; 1.614375, 3.30946875, 6.7844109375. option E

Arithmetic and Geometric series

• a1 = 1458
• r = 1/3
• a6 = 6

S6 = a(rⁿ - 1) / r -1

= 1468(1/3^6 - 1) / (1/3 - 1)

= 1468(0.00137174211248 - 1) / -2/3

= 1468(-0.9986282578875) / -0.66666666666666

= -1,465.98628257885 / -0.66666666666666

= 2198.97942386829

Approximately,

S6 = 2199

Arithmetic series

• a36
• a1 = 27
• d = -5/2

Sn = n/2{2a + (n -1)d}

= 36/2 {2×27 + (36-1)-5/2}

= 18{54 + (35)-5/2}

= 18(54 + 175/2)

= 18(54 + 87.5)

= 18(141.5)

s36 = 2547

a36 = a + (n - 1) d

= 27 + (36 - 1)-5/2

= 27 + (35)-5/2

=27 + -175/2

= 27 - 87.5

= -60.5

S20 = n/2{2a + (n -1)d}

= 20/2{2×27 + (20-1)-5}

= 10(54 + (19)-5)

= 10{54 + (-95)}

= 10(54-95)

= 10(-41)

s20 = -410

Missing terms of the geometric sequence:

nth term = ar^n-1

448/135 = 63/80×r^(6-1)

448/135 = 63/80×r^5

r^5 = 448/135 ÷ 63/80

= 448/135 × 80/63

= 35,840/8,505

r = 5√35,840/5√8505

= 946.57/461.11

r = 2.05

Second term = a×r

= 63/80×2.05

= 1.614375

Third term = ar²

= 63/80×2.05²

= 63/80×4.2025

= 3.30946875

Fourth term = 63/80 × 2.05³

= 63/80×8.615125

= 6.7844109375

Therefore, none of these are correct

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