Arithmetic Sequences - Gold

A number sequence has the nth term, 150-3n.

What would the 10th term be?

A number sequence has the nth term, 150-3n.

Calculate the term number which will be the first negative number in the sequence.

Answer explanation

When 150-3n=0

-3n=-150

n=50

Therefore the 51st term will be the first negative term

Lucy has a charm necklace with 30 charms on it. Every month she adds two new charms onto the necklace. How many charms will there be on the necklace after 2 years?

Answer explanation

The nth term is

30 + 2n

Two years = 24 months

After 24 months =

30 + (2*24) = 30 + 48

= 78

The nth term of a sequence is -5n+2.

Which term of the sequence is equal to -23?

Answer explanation

-5n+2=-23

-5n=-25

n=5

The nth term of a sequence is 2n-1.

Which term of the sequence is equal to 23?

Answer explanation

2n-1=23

2n=24

n=12

The nth term of a sequence is 2n-20.

If the last term in the sequence is 180, how many terms are in the sequence?

Answer explanation

2n-20=180

2n=200

n=100

The first five terms in a sequence are 4, 7, 10, 13, 16.

The 100th term is 301.

What is the value of the 98th term?

Answer explanation

n: 1 2 3 4 5

s: 4 7 10 13 16

d: 3 3 3 3 3

dxn: 3 6 9 12 15

s-dn: 1 1 1 1 1

nth term = 3n+1

If n = 98,

(3x98)+1 =

294+1=

295

Bob throws a coin from the edge of a cliff.

It takes a second for the coin to have fallen 16 feet. A second later, it has fallen 48 feet and after three seconds, 80 feet.

How many feet will the coin have fallen after 6 seconds?

Answer explanation

n: 1 2 3

s: 16 48 80

d: 32

dxn: 32 64 96

s-dn: -16

nth term = 32n-16

If n = 6,

32x6 - 16 =

192 - 16 =

176

A house worth £350,000 when purchased was worth £335,000 after a year, and £320,000 after a second year.

If the economy does not pick up and this trend continues, how much will the house be worth after six years?

Answer explanation

n: 1 2 3

s: 350 335 320

d: -15

dxn: -15 -30 -45

s-dn: 365

nth term = 365-15n

If n = 7, (as 1 = year 0)

365 - (15*7) =

365 - 105 =

260

A bookshelf has seven shelves of different widths. Each shelf is narrower than the shelf below it. The bottom shelves are 26cm, 31cm and 36cm wide. How many cm wide is the top shelf?

Answer explanation

n: 1 2 3

s: 36 31 26 (remember the shelves get wider as they go down)

d: -5

d x n: -5 -10 -15

s-dn: 41

nth term: 41 -5n

Top shelf = 7

41 - (5*7) =

41 - 35 =

6