EXERCISE 7 (b)
A sequence { an} is given by the formula an= 10 - 3 n, ne N. Prove that it is an A.P.
Answers
Answered by
1
Let 1 = n,
a(1)= 10-3(1) =7
Let 2= n,
a(2)= 10-3(2)=4
Let 3= n,
a(3)= 10-3(3)=1
From this, we get the sense that a=10, and common difference is -3.
To further prove that this holds true for any and all natural numbers,
Let some k=n such that k belongs to N
a(k) =10-3(k)
Now if an is actually an AP, k+1 is also a part of the AP.
a(k+1) =10-3(k+1)
=10-3(k)-3
Where -3 is the common difference.
Hence, for all n belongs to N, given an for an Arithmetic Progression.
Hope this was helpful
a(1)= 10-3(1) =7
Let 2= n,
a(2)= 10-3(2)=4
Let 3= n,
a(3)= 10-3(3)=1
From this, we get the sense that a=10, and common difference is -3.
To further prove that this holds true for any and all natural numbers,
Let some k=n such that k belongs to N
a(k) =10-3(k)
Now if an is actually an AP, k+1 is also a part of the AP.
a(k+1) =10-3(k+1)
=10-3(k)-3
Where -3 is the common difference.
Hence, for all n belongs to N, given an for an Arithmetic Progression.
Hope this was helpful
Similar questions