Difference AP

Calculate the difference of arithmetic progression if the sum of its first 19 members Sn = 8075 and the first member is a1 = 20

Result

d =  45

Solution:

S=na1+an2 8075=1920+20+(191)d2 850=220+(191)d 810=18d d=45 S=20+65+110+155+200+245+290+335+380+425+470+515+560+605+650+695+740+785+830=8075S = n \dfrac{ a_1 +a_n}{2} \ \\ 8075 = 19 \dfrac{ 20 +20 +(19-1)d }{2} \ \\ 850 = 2\cdot 20 + (19-1)d \ \\ 810 = 18 d \ \\ d = 45 \ \\ S = 20 + 65 + 110 + 155 + 200 + 245 + 290 + 335 + 380 + 425 + 470 + 515 + 560 + 605 + 650 + 695 + 740 + 785 + 830 = 8075



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