Question

Find the sum of first 100 terms of the arithmetic sequence, 50,40,30,...

Answer 1

Answer:

100th therm is -44500

Step-by-step explanation:

arithmetic sequence 50,40,30,...

first term, a₁ , f = 50

                  a₂ = 40

                  a₃ = 30

common difference = a₂-a₁

                               = 40-50

                               = -10

nth term, Xₙ = dn+(f-d)

                   = -10n+(50- -10)

                   = -10n+(50+10)

                   = -10n+60

                   = 60-10n

100th term  = 60 -(10x100)

                  = 60-1000

                  = -940

sum, Sₙ = $\frac{n[first term+last term]}{2}$

     S₁₀₀ = $\frac{100[first term+ 100th term]}{2}$

            = 50x [firt term+100th term]

            = 50x [50+-940]

            = 50x -890

            = -44500