The 38th term of the sequence with first term 5 is 1,350,851,717,672,992,091. This can be solved using the concept of both arithmetic sequence and arithmetic series. If we will use the concept of arithmetic sequence. To fill the missing terms we will use the condition that each term is triple the previous term decreased by 4.
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Arithmetic Series and Sequence:
The 38th term of the sequence with first term 5 is 1,350,851,717,672,992,091. This can be solved using the concept of both arithmetic sequence and arithmetic series. If we will use the concept of arithmetic sequence. To fill the missing terms we will use the condition that each term is triple the previous term decreased by 4.
Solutions:
a₁ = 5
a₂ = 3(5) - 4 = 15 - 4 = 11
a₃ = 3(11) - 4 = 33 - 4 = 29
a₄ = 3(29) - 4 = 87 - 4 = 83
a₅ = 3(83) -4 = 249 - 4 = 245
a₆ = 3(245) - 4 = 735 - 4 = 731
a₇ = 3(731) - 4 = 2193 - 4 = 2,189
a₈ = 3(2189) - 4 = 6567 - 4 = 6,563
a₉ = 3(6563) - 4 = 19689 - 4 = 19,685
a₁₀ = 3(19685) - 4 = 59055 - 4 = 59,051
a₁₁ = 3(59051) - 4 = 177153 - 4 = 177,149
a₁₂ = 3(177149) - 4 = 531447 - 4 = 531,443
a₁₃ = 3(531443) - 4 = 1594329 - 4 = 1,594,325
a₁₄ = 3(1594325) - 4 = 4782975 - 4 = 4,782,971
a₁₅ = 3(4782971) - 4 = 14348913 - 4 = 14,348,909
a₁₆ = 3(14348909) - 4 = 43046727 - 4 = 43,046,723
a₁₇ = 3(43046723) - 4 = 129140169 - 4 = 129,140,165
a₁₈ = 3(129140165) - 4 = 387420495 - 4 = 387,420,491
a₁₉ = 3(387420491) - 4 = 1162261473 - 4 = 1,162,261,469
a₂₀ = 3(1162261469) - 4 = 3486784407 - 4 = 3,486,784,403
a₂₁ = 3(3486784403) - 4 = 10460353209 - 4 = 10,460,353,205
a₂₂ = 3(10460353205) - 4 = 31381059615 - 4 = 31,381,059,611
a₂₃ = 3(31,381,059,611) - 4 = 94,143,178,833 - 4 = 94,143,178,829
a₂₄ = 3(94,143,178,829) - 4 = 282,429,536,487 - 4 = 282,429,536,483
a₂₅ = 3(282,429,536,483) - 4 = 847,288,609,449 - 4 = 847,288,609,445
a₂₆ = 3(847,288,609,445) -4 = 2,541,865,828,335 - 4 = 2,541,865,828,331
a₂₇ = 3(2,541,865,828,331) - 4 = 7,625,597,484,993 - 4 = 7,625,597,484,989
a₂₈ = 3(7,625,597,484,989) - 4 = 22,876,792,454,967 - 4 = 22,876,792,454,963
a₂₉ = 3(22,876,792,454,963) - 4 = 68,630,377,364,889 - 4 = 68,630,377,364,885
a₃₀ = 3(68,630,377,364,885) - 4 = 205,891,132,094,655 - 4 = 205,891,132,094,651
a₃₁ = 3(205,891,132,094,651) - 4 = 617,673,396,283,953 - 4 = 617,673,396,283,949
a₃₂ = 3(617,673,396,283,949) - 4 = 1,853,020,188,851,847 - 4 = 1,853,020,188,851,843
a₃₃ = 3(1,853,020,188,851,843) - 4 = 5,559,060,566,555,529 - 4 = 5,559,060,566,555,525
a₃₄ = 3(5,559,060,566,555,525) - 4 = 16,677,181,699,666,575 - 4 = 16,677,181,699,666,571
a₃₅ = 3(16,677,181,699,666,571) - 4 = 50,031,545,098,999,713 - 4 = 50,031,545,098,999,709
a₃₆ = 3(50,031,545,098,999,709) - 4 = 150,094,635,296,999,127 - 4 = 150,094,635,296,999,123
a₃₇ = 3(150,094,635,296,999,123) - 4 = 450,283,905,890,997,369 - 4 = 450,283,905,890,997,365
a₃₈ = 3(450,283,905,890,997,365) - 4 = 1,350,851,717,672,992,095 - 4 = 1,350,851,717,672,992,091
Therefore, the 38th term of the sequence is 1,350,851,717,672,992,091.
What are sequences: brainly.ph/question/594377
What are the types of sequences: brainly.ph/question/658398
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