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* 4 Sequences Ry Garis, L Goquenca 2 of Soque nee VW & 4 unclisw OL Narlterak numbers wicth — coolsmasw is the Set of Roat numbers os compXox numbers, A nmap bing Fen>e then fin) = ta nen Gs Ca tle a Sequence to be cdenoled it by $F 0), $m FO) Fe ferta Ang © Uhed Qeates % ‘By adcting or subtracting -the -Ler-rmns at Q@ sequence then we yet as Qerfes , Saquence by VAC ler sive. wrehoTorr & ae. Opay SH) Ahr Ones a oe hn Bnas at An Ores + (-4) : + Avtthmetf(e Sequener é A Paqucnce whose -loams INET Pas 2 OT decrease oy Q fined unimber, Sf {Avda sta oF Fe suck thet 4y-ty)..> comptamt WV REN , Hem Ws Qn Avtthmetic Seq ive Ce: enth Aevrm of APS The At (n=-1)dk, = Sy- Shea e nth dorm from lasts Tis 7 (n-)a. [tL last term), oe Sum of \rst on -terms! s + QO }Rost She a [ 2a + Cr-1 a | | re = a [a+r] ol —= Commsw owm/ AzlLavence- Sayoshich Saha + Simp. ports ow APS, do 5A, Ay ys, are WM AP, thew ) Aik, Atk, ark 9700 aksa an AP. b) QK, 2K, 0,%K oe also 1 AP, ui) Of Oy, 024+. AR YW, ba,+s GL Jwo AP9 , thn a) a, +b, 1A tb, pose Ore ON AP, ») Qyby, Orbe... arantkim AP, tes ft a my ii) a,= RE Ore , OK 4n-k. ty) In+l! wnumbors m AP con be taken as Aa-PHA , G-(H-1) Ayu, AA, a, AAs OF (r-DA, arth ») om numbers mm AP can be ‘taken as [ a-(2e-Na 5 a- (am-3)d,..., GIA, ad, att, o4+ ah. , GA C2r-3)r, at (ar-)aT, vi) 3F wie lew of any gogponc tS Umcos amxpressin an Ww Cont b) Ave — gayeoncr ts AP. vi) S¢ Surv of, ue terms vk amy — aesue ree Ke qradrarte onpesstory 1 W, (an bu+e) jy Sagqntamee FE On VAP, 4 Goometaic Sequence ° A Sospee nice where the vatto tM Ory form and ety ost precoding dorm fs enwtant Thus , tydasday oo qP , then Comma = mi45 grotto nw han Pe Sayochich Saha Sayoshish Saha i) If Gy) Oy) Hy prs Ro by, barbarism two GPs then, ) Qh) 1 Anb,, Agbg, +>. Ri Wb,» O4/ bo» arte 7H GP . ® Q,+ b, , Apt Prose: aa not @P. witlon as wy) (2m! humbars mm GP cam ba Wre"e m-] im Poh? OF ite i tn oF A Chg Or yoke | OF Zen written as 6 wy) Dw numbers % GP can be a a @ By On ar... ne2ne! > n= 7 “RA op OF om — Im-3 avr Ose ? where the * Hormeic Sequonce ! A\ Sequence Tecipro cars of Hs derms aw an AP, SF Oy, O,,..., 4, Oe wm AP, Yar Yasy > Zan we In HP. enth stevm , Tre a ee 2. Ay Ap i td = =a 4H) Gea) a+ (n-1) (4-4). ay, a2 An 0) & ~ a, (h-t) (a - 42) / ent term {oom end, Tn = eno -leom of HP can be zero, & {hene?S nO Generar formu — foe fencing out the sum of nclerms ab HP. ef % 22,259 Fn are qn HP , ther 2 a x, % KyXo + Kary +o + @y-1% = Chris ™n eo avary 4erm of a HP te multiplied or divided by Some now Ferd faxed quantity , the oes wing prog ressiow 3 HP. M - x Recog nétton of AP, GP RHP If a,b,c aw % gc, COSSTVa, looms oh A Sdquenee , Then, a-b a AP — whe ————s) SS b-¢ a a-b . @ GP — when Tar He -— when aA-b & —- b- @ 4 Heanss a, Aatthmette Hean: Sf ob,6 dre ™ on ba the AN ok 2™ S- *) Sing le AU of. 1 op es va warbegers Q,4+AQg+->- +n < a ee AW “i i) nm AMs pedween two numbers: Q, Ay, Aa, -.s , Any A= ate Cran)’ b. Gaonne-teic Uecan ¢ St Qa, bo aw ™ qP, lb ps cthe GM of ake : Si myles GH al, a8) +Y2 Num a Gu > (2 GrQ,-- a a ot GHs betwean 2 numbezrs f Q Gr Gar Ga y0- > Gn»b h («) wel Qa Sayoshich Saha % ae Notodton! }) 2 donde. eee i) = afd) = a £90), ii) BLI@ #4} = 2,40) + 2 q(t). . 4 Srenbpor-towt results ° a) ane ny), b) ain’ ne ¢) s oS f ons) }* i x Netthimetco — Geomelte Gooiess (AGS). avithmaette o — 4) gantes & catch +o be am 2gome we Series th He cach term by re WAH ert the cosrespbondiry seem iid am @ Stem of m termes & hormed } + 3x 4 Sut Fx + AP J ; og . of on AGS ? g Sy js: oe(!- =a a [a+ ch- Dayo” = [om i-? oL the AGS 4, Cord)a, (oradye, 4 Dar(n-a] a When 4p nft 4 fist + Sing soaty [ie mnt] ” Cs = —_ + Av - (i= on) & Method of Aikhersamces Sf -the “difhovences of the Juccessive terms sf @ garies nth dorm ok the qsa an AP ow GP we. cow bind Sevias | the wlepy — Sayochich Saha ) Ponmte tha nth term QR the gum ok the Jeaies ato n lerme ot the g2e%es by Ty & Ym weabecrlively. 1) Ro wattle the given Sea4es wre sack torm ghiftak by — one. plane to the wight. ) Yubtoacctry dhe above two forme af hey Opies , {and The: * Va Vr mmothot$ Let Th, Ta, Ty,--. ba the terms of a Semsanca , tf there oxisty oO Sequence Vy 5920 Vg oo Satta tym} Te = Uy Vy s we nm K pl, ten 8,5 She SS (vw - ards ne = ( kT Pant 4 Wergtted Means$ Let 045 Op oy An be positive weak numbers Ro wy,We,-s We be vaktforal whumbeara | Chen we cdefane weighted asttinetioc nmgan (4*) ; weight aL geometnic moon (G*) A wee 2d hoymeanic aman (#*) as. = Ula Vee iP QW, + AgWo ts. + OnWe Wy Wo + 0. + Wy L x G = (ay. a,™, aly an) Nyt Wate 4 Ww Ht e With, to... tWa Baer We a 2 Wr. Qy An On * 4a : . >> gt > Ww [ Squatity holds at sither
