This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Hili ni swali kuhusu Mfululizo wa Kihesabu (Arithmetic Progression - AP). Tunahitaji kupata jumla ya vigezo 10 vya kwanza. Formula ya jumla ya n vigezo vya kwanza vya AP ni: S_n = (n)/(2)[2a + (n-1)d] ambapo a ni kigezo cha kwanza, d ni tofauti ya kawaida (common difference), na n ni idadi ya vigezo. Step 1: Tambua kigezo cha kwanza (a) na tofauti ya kawaida (d). Kutoka kwa mfululizo 8, -1, -10, -19, : Kigezo cha kwanza a = 8. Tofauti ya kawaida d = -1 - 8 = -9. Unaweza pia kuthibitisha: d = -10 - (-1) = -10 + 1 = -9. Idadi ya vigezo n = 10. Step 2: Badilisha vigezo hivi kwenye formula ya jumla ya AP. S_10 = (10)/(2)[2(8) + (10-1)(-9)] Step 3: Fanya hesabu ndani ya mabano. S_10 = 5[16 + (9)(-9)] S_10 = 5[16 - 81] Step 4: Rahisisha zaidi. S_10 = 5[-65] S_10 = -325 Jumla ya vigezo 10 vya kwanza ni: -325 Last free one today — make it count tomorrow, or type /upgrade for unlimited.