Question 1

Topic: Arithmetic Progression (9709 P1)

[Total: 6 Marks]

The second term of an arithmetic progression is 12.
The sum of the first 8 terms is 216.
Find the first term $a$ and the common difference $d$.

Part (i): Form an equation using the second term. [1 mark]

Using $u_n = a + (n-1)d$, complete the equation for the 2nd term:

1$a$ + $d$ =

The formula is $u_2 = a + (2-1)d$. The value is given in the text.

Part (ii): Form a simplified equation using the Sum. [2 marks]

Using $S_n = \frac{n}{2}(2a + (n-1)d)$ for $n=8$:

$$ S_8 = \frac{8}{2}(2a + 7d) = 216 $$

Simplify this equation ($4(2a+7d) = 216$) to find the values for the boxes below:

$a$ + $d$ =

Divide the total sum (216) by 4 first to simplify the brackets.

Part (iii): Solve the simultaneous equations. [3 marks]

You now have:

1) $a + d = 12$
2) $2a + 7d = 54$

Common Difference ($d$) =

First Term ($a$) =

Rearrange eq (1) to $a = 12 - d$ and substitute it into eq (2).

Question Complete!
You have mastered Simultaneous AP problems.