find the terms34th term of a.p. if d=3 and a1=1 too many terms to calculate another method?

Expert Answers
hala718 eNotes educator| Certified Educator

You do not need to write all the terms in order to determine the 34th terms.

All you need to do is to use the formula to find any nth terms in the progression.

Let a1, a2, a3, ........., a34 be terms in an A.P such that:

a1= 1   and the common difference d = 3

We know that:

an = a1 + (n-1)*d

We need to determine the 34th term.

We will substitute with given values.

==> a34 = a1+ (34-1) * d

==> a34 = 1 + 33*3

==> a34 = 1 + 99 = 100

==> a34 = 100

giorgiana1976 | Student

If you know the value of the first term and the common difference, you can calculate what term dou you want, from the given a.p.

It is no need to calculate all previous terms from the a.p., to determine the wanted term.

We'll recall the fomrula for the general term. This formula will help you to determine what term do you need:

an = a1 + (n-1)*d

We'll put n = 34

a34 = a1 + (34 - 1)*3

a34 = 1 + 33*3

a34 = 1 + 99

a34 = 100

So, as you can see, it is so easy and it takes just few steps to determine any term you want.