Question

how to find the position of a term in an arithmetic sequence​

Answer 1

Answer:

position of term a = a+(n-1)d where a is the first term, d is the common difference and n is the value of a

Answer 2

The given question is how to find the position of a term in an arithmetic sequence.

An arithmetic progression also called arithmetic sequence is a sequence of numbers.

The difference between the consecutive terms is constant.

For instance, the sequence 1,3,5, 7, 9, 11, 13, 15,17,19,21,...... . is an arithmetic progression with a common difference of 2.

It is an ordered set of numbers that have a common difference between each consecutive term.

The nth term of an arithmetic sequence is given by

an = a + (n – 1)d.

so that we have to find the position of a term in an arithmetic sequence.

let us consider an example sequence, 1,5,9,13,....., 153...

...

In the above sequence, we have to find the position of the number 153.

The first term a = 1.

The common difference d is 4.

The position of the term is to be found in 153.

let us substitute the values in the formula, we get

$153 = 1 + (n - 1)4$

The value 4 gets multiplied by n-1.

$153 = 1 + 4n - 4 \\ 153 = 4n - 3$

The 3 subtracting on the right side move to the left side by addition,

$153 + 3 = 4n \\ 156 = 4n \\ \frac{156}{4} = n$

The value of n will be

$156 \div 4 = 39$

Therefore, the number 153 lies in position 39.

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