Diketahui barisan geometri un, dengan u2+1 adala...

Pertanyaan

Diketahui barisan geometri $u_n$ , dengan $u_2+1$ adalah rata-rata $u_1$ dan $u_3$ . Jika $u_1=8$ maka jumlah 4 suku pertama yang mungkin adalah....

D. Kamilia

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

$straight u subscript 2 plus 1 space adalah space rata minus rata space straight u subscript 1 space dan space straight u subscript 3 comma space maka straight u subscript 2 plus 1 equals fraction numerator straight u subscript 1 plus straight u subscript 3 over denominator 2 end fraction 2 straight u subscript 2 plus 2 equals straight u subscript 1 plus straight u subscript 3 Karena space straight u subscript straight n space adalah space barisan space geometri comma space maka box enclose 2 ar plus 2 equals straight a plus ar squared end enclose Selanjutnya straight u subscript 1 equals 8 rightwards arrow box enclose straight a equals 8 end enclose Maka 2 ar plus 2 equals straight a plus ar squared 2 left parenthesis 8 right parenthesis straight r plus 2 equals left parenthesis 8 right parenthesis plus left parenthesis 8 right parenthesis straight r squared 16 straight r plus 2 equals 8 plus 8 straight r squared 8 straight r squared minus 16 straight r plus 6 equals 0 4 straight r squared minus 8 straight r plus 3 equals 0 left parenthesis 2 straight r minus 3 right parenthesis left parenthesis 2 straight r minus 1 right parenthesis equals 0 box enclose straight r equals 3 over 2 end enclose space atau space box enclose straight r equals 1 half end enclose Jika space straight r equals 3 over 2 comma space maka$

Sehingga space straight S subscript 4 equals straight u subscript 1 plus straight u subscript 2 plus straight u subscript 3 plus straight u subscript 4 equals 8 plus 12 plus 18 plus 27 equals box enclose 65 Jika space straight r equals 1 half comma space maka