# Sequences and Series. AQA C2 Pg.175 Q6.b) Find the sum of the first terms of the.....

• Feb 28th 2010, 02:36 PM
ansonbound
Sequences and Series. AQA C2 Pg.175 Q6.b) Find the sum of the first terms of the.....
6. An arithmetic series has sixth term 28 and tenth term 44.
a) Find the first term and the common difference.
U6 = a + (6-1)d, 28 = a +5d---(1)
U10 = a + (10-1)d, 44 = a + 9d---(2)

(1) - (2)

16 = 4d
d = 4
a = 15 - 5 * 4
a = 8

b.Find the sum of the first terms of the series.
(Doh)?????

• Feb 28th 2010, 02:57 PM
masters
Quote:

Originally Posted by ansonbound
6. An arithmetic series has sixth term 28 and tenth term 44.
a) Find the first term and the common difference.
U6 = a + (6-1)d, 28 = a +5d---(1)
U10 = a + (10-1)d, 44 = a + 9d---(2)

(1) - (2)

16 = 4d
d = 4
a = 15 - 5 * 4
a = 8

b.Find the sum of the first terms of the series.
(Doh)?????

Hi ansonbound,

How many terms do you want to find the sum of?

Where do you want to start $\displaystyle a_1)$, and where do you want to end $\displaystyle (a_n)$

The sum of an arithmetic series is

$\displaystyle S_n=\frac{n}{2}(a_1+a_n)$

Just fill in what you know and solve for the sum.
• Feb 28th 2010, 03:07 PM
ansonbound
The answer at the back of the book is 5300.(Nerd)??
• Feb 28th 2010, 03:15 PM
masters
Quote:

Originally Posted by ansonbound
The answer at the back of the book is 5300.(Nerd)??