Question

how many terms of the AP 2,10,18... must be taken to give the sum 90 (4)marks question

Answer 1

SOLUTION:

a= 2

d = 10-2 = 8

Sn = 90

Sn = n/2[2a + (n-1)d

Sn = n/2[4+ (n-1)8]

Sn = 2n + 4n ( n-1)

90 = 4n² -2n

4n² -2n -90=0

2n² - n- 45=0

2n² - 10n +9n - 45=0

2n ( n-5)+ 9(n-5)=0

(n-5)(2n+9) =0

therefore n = 5 or n= -9/2

we will cancel n= -9/2 because it is in negative.

So, n = 5

ANSWER: number of terms must be taken to give the sum 90 = 5