Question

In an Arithmetic Progression (A.P.), the fourth and sixth terms are 8 and 14 respectively. Find the:

1. first term 
2. common difference 
3. sum of the first 20 terms.

Answer 1

Let a and d be the first term and common difference.

$$a + 3d = 8$$ and $$a + 5d = 14$$. 

Subtracting: $$2d = 6 \Rightarrow d = 3$$. 

Then $$a + 9 = 8 \Rightarrow a = -1$$.

$$S_{20} = \frac{20}{2}[2(-1) + 19(3)]$$

$$= 10(-2 + 57)$$

$$= 550$$