Question

If the first and the last term of an arithmetic progression, with common difference

Answer 1

The number of terms in the given arithmetic sequence is n = 10. Using the given first, last term, and the common difference of the arithmetic sequence, the required value is calculated.

What is the nth term of an arithmetic sequence?

The general form of the nth term of an arithmetic sequence is

an = a1 + (n - 1)d

Where,

a1 - first term

n - number of terms in the sequence

d - the common difference

Calculation:

The given sequence is an arithmetic sequence.

First term a1 = $1\frac{1}{2}$ = 3/2

Last term an = $2\frac{1}{2}$ = 5/2

Common difference d = 1/9

From the general formula,

an = a1 + (n - 1)d

On substituting,

5/2 = 3/2 + (n - 1)1/9

⇒ (n - 1)1/9 = 5/2 - 3/2

⇒ (n - 1)1/9 = 1

⇒ n - 1 = 9

⇒ n = 9 + 1

∴ n = 10

Thus, there are 10 terms in the given arithmetic sequence.

learn more about the arithmetic sequence here:

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Question: If the first and the last term of an arithmetic progression with a common difference are $1\frac{1}{2}$, $2\frac{1}{2}$ and 1/9 respectively, how many terms has the sequence?