Question

Given an arithmetic series if the number of 8 first tribe 100 and the number 12 the first tribe 222 then the 6th tier of the series is .....

Answer 1

// a = first term

b = differences between tribes

Un = tribe to n

Sn = number of first n tribes //

// search for 2a //

Sn = n / 2 (2a + (n - 1) b

S8 = 8/2 (2a + (8 - 1) b)

(100) = 4 (2a + 7b)

100 = 8a + 28b

8a = 100 - 28b // divided by 4 all //

2a = 25 - 7b

// finds b by substituting 2a //

S12 = n / 2 (2a + (n - 1) b)

S12 = (12) / 2 ((25 - 7b) + (12 - 1) b)

(222) = 6 (25 - 7b + 11b)

222/6 = 25 + 4b

4b = 37 - 25

b = 12/4

b = 3

// find a by substituting b //

2a = 25 - 7b

2a = 25 - 7 (3)

2a = 25 - 21

a = 4/2

a = 2

// searches for 6th /

Un = a + (n - 1) b

U6 = (2) + (6 - 1) (3)

U6 = 2 + 5 (3)

U6 = 2 + 15

U6 = 17

So the sixth row is 17