Jumlah 5 suku pertama deret aritmatika adalah 65 dan suku ke-7 adalah 25 tentukan suku ke-15

Jawaban:

jumlah 5 suku pertama :

U1 = a

U5 = a + 4b

Sn = n/2 (a + Un)

S5 = 5/2 (a + a + 4b)

S5 = 5/2 (2a + 4b)

= 5(a + 2b)

= 5a + 10b

5a + 10b = 65

a + 6b = 25

5a + 10b = 65

5a + 30b = 125

______________ –

-20b = -60

20b = 60

b = 60/20

b = 3

a + 6b = 25

a + 6(3) = 25

a + 18 = 25

a = 25 – 18

a = 7

U15 = a + 14b

= 7 + 14(3)

= 49

Jawab:

49

Penjelasan dengan langkah-langkah:

U1 = a

U5 = a + 4b

Sn = n/2 (a + Un)

S5 = 5/2 (a + a + 4b)

S5 = 5/2 (2a + 4b)

= 5(a + 2b)

= 5a + 10b

5a + 10b = 65

a + 6b = 25

5a + 10b = 65

5a + 30b = 125

______________ –

-20b = -60

20b = 60

b = 60/20

b = 3

a + 6b = 25

a + 6(3) = 25

a + 18 = 25

a = 25 – 18

a = 7

U15 = a + 14b

= 7 + 14(3)

= 49