Question

FORM THREE - 2021

1. The fourth term of an AP is twice as great as the third term and the 12th term is 30. Find;
(a) The sum of the first 20 terms
(b) The common difference​

Answer 1

See explanation

Step-by-step explanation:

Fourth term = 2 * third term

a + 3d = 2(a + 2d)

a + 3d = 2a + 4d

a - 2a = 4d - 3d

- a = d

d = - a

12th term = 30

a + 11d = 30

Substitute d = -a

a + 11d = 30

a + 11(-a) = 30

a - 11a = 30

-10a = 30

a = 30/-10

a = -3

Recall,

- a = d

-(-3) = d

3 = d

Sum of the first 20 terms

S20 = n/2{2a + (n - 1)d}

= 20/2{2*-3 + (20-1)3}

= 10{-6 + (19)3)

= 10(-6 + 57)

= 10(51)

= 510

Sum of the first 20 terms = 510