Jawaban:

Diketahui suatu barisan aritmetika dengan U subscript 3 equals 36 dan U subscript 5 plus U subscript 7 equals 144. Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell U subscript n end cell equals cell a plus left parenthesis n minus 1 right parenthesis b end cell row blank blank blank row cell U subscript 3 end cell equals cell a plus left parenthesis 3 minus 1 right parenthesis b end cell row 36 equals cell a plus 2 b space....... space left parenthesis 1 right parenthesis end cell row blank blank blank row cell U subscript 5 plus U subscript 7 end cell equals cell a plus left parenthesis 5 minus 1 right parenthesis b plus a plus left parenthesis 7 minus 1 right parenthesis b end cell row 144 equals cell 2 a plus 4 b plus 6 b end cell row 144 equals cell 2 a plus 10 b space... space left parenthesis 2 right parenthesis end cell end table

Eliminasi (1) dan (2), sehingga:

table row cell a plus 2 b equals 36 end cell cell open vertical bar cross times 2 close vertical bar end cell cell 2 a plus 4 b equals 72 end cell row cell 2 a plus 10 b equals 144 end cell cell open vertical bar cross times 1 close vertical bar end cell cell 2 a plus 10 b equals 144 space minus end cell row blank blank cell negative 6 b equals negative 72 end cell row blank blank cell b equals fraction numerator negative 72 over denominator negative 6 end fraction end cell row blank blank cell b equals 12 end cell end table

Untuk menentukan a, substitusikan b equals 12 ke salah satu persamaan yaitu a plus 2 b equals 36, sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell a plus 2 b end cell equals 36 row cell a plus 2 cross times 12 end cell equals 36 row cell a plus 24 end cell equals 36 row a equals cell 36 minus 24 end cell row a equals 12 end table

Maka;

table attributes columnalign right center left columnspacing 0px end attributes row cell S subscript n end cell equals cell n over 2 open parentheses 2 a plus left parenthesis n minus 1 right parenthesis b close parentheses end cell row cell S subscript 10 end cell equals cell 10 over 2 cross times open parentheses 2 cross times 12 plus left parenthesis 10 minus 1 right parenthesis cross times 12 close parentheses end cell row blank equals cell 5 cross times left parenthesis 24 plus 9 cross times 12 right parenthesis end cell row blank equals cell 5 cross times left parenthesis 24 plus 108 right parenthesis end cell row blank equals cell 5 cross times left parenthesis 132 right parenthesis end cell row blank equals 660 end table

Jadi, jumlah sepuluh suku pertama deret tersebut adalah 660.