Question

:) Consider the arithmetic sequence -1,-4, -7.-10... a) What is the common difference of this sequence? b) Write the algebraic form of this sequence?​

Answer 1

Given : AP is -1,-4, -7.-10...  

To find : Common difference of the AP and it's algebraic form.

Solution :

Common difference:

Common difference of an AP is given by the difference of its any two consecutive terms - Like a2 - a1 or a3 - a2 etc. where a1, a2 and a3 are consecutive terms of AP. Common difference is always same through out the whole sequence.

In the given AP, consider first two terms.

• a1 = -1
• a2 = -4

Common difference = a2 - a1 = -4+1 = -3

So the common difference is -3.

Algebaric form of sequence:

The general expression to denote nth term of an AP is an = a + (n-1)d where an is nth term, a is first term, d is common difference and n is the number of terms.

We have a = -1 and d = -3

So nth term is given by,

an = -1 + (n-1)(-3)

an = -1 -3n + 3

an = 2 - 3n

This is the algebraic form of sequence.[tex][/tex]