Question

Write down in terms of n,an expression for the Nth term of the following sequences.

A) 2,5,8,11,14
B) 9,11,13,15,17

Answer 1

so for question a the ans is 3n-1

for question b the ans is 2n+7

Explanation:

Question A

using the formula for arithmetic progressikn(a.p) a +(n-1)d, u use this formula because it has a common differnce

a=2, where a is first term or t1

d=t2-t1=5-2=3m where d is common difference

replace the values in the formula

2+(n-1)3

2+3n-3

3n-3+2

3n-1, this is the formula for the nth term

it will be 3n -1

if u try it

3(1)-1=2

3(2)-1=5

3(3)-1=8

3(4)-1=11

3(5)-1=14

Question B

using the formula for a.p, a+(n-1)d

a=9, because it is the first term

d=t2-t1=11-9=2

replace the values in the formula

9+(n-1)2

9+2n-2

2n+9-2

2n +7,this is the formula for the7th term

if u try it

2(1)+7=9

2(2)+7=11

2(3)+7=13

2(4)+7=15

2(5)+7=17

Answer 2

see explanation

Explanation:

The n th term of an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

A

There is a common difference d between consecutive terms , that is

d = 5 - 2 = 8 - 5 = 11 - 8 = 14 - 11 = 3

Thus the sequence is arithmetic with a₁ = 2 and d = 3, then

`a_(n)` = 2 + 3(n - 1) = 2 + 3n - 3 = 3n - 1

`a_(n)` = 3n - 1

B

There is a common difference d between consecutive terms , that is

d = 11 - 9 = 13 - 11 = 15 - 13 = 17 - 15 = 2

Thus the sequence is arithmetic with a₁ = 9 and d = 2 , then

`a_(n)` = 9 + 2(n - 1) = 9 + 2n - 2 = 2n + 7

`a_(n)` = 2n + 7