Find the 32 nd term of each sequence. 23,30,37,44, ...........

In mathematics, an arithmetic progression (AP) is a list and possibly sequence of numbers where each term is collected by adding a sequence towards the term before it.

The fixed number, without regard to arithmetic progression, is signified by the letter 'd.'
Common difference => d = a2 - a1 = a3 - a2 = a4 - a3 =...... = a - an-1.
nth term of AP: an = a + (n - 1) d
The sum of n terms of an AP's => Sn = n/2(2a+(n-1)d) = n/2(a + l), where l = last term of the AP.

Finally, here is the answer to the question:

The following are the numbers with in displayed sequence:

23,30,37,44, ...........

The 32nd number in the series must be investigated because it contains 32 terms.

The common difference between two consecutive terms of an AP that are equal is denoted by the letter 'd.'

Let's consider the first term is'a₁' = 23.

Let's consider 'a₂' = 30 is the second term.

Let's consider the third term is 'a₃' = 37.

Substitute the values the above obtained equation; the 32nd term is-

d = a₂ - a₁

Estimate the common difference;

d = 30 - 23

d = 7

Substitute the values in the next formula; the 32nd term is

The formula given will estimate the nth term equation;

nth term of an AP: an = a + (n - 1) d

Total number of terms ; n = 32

Initial term is a = 23

Common difference d = 7

Substitute the given values in nth term formula;

a₃₂ = a + (n - 1) d

a₃₂ = 23 + (32 - 1)(7)

a₃₂ = 23 + 217

a₃₂ = 240

Thus, the 32nd term value of the given arithmetic sequence is estimated to be 240.

More information on the arithmetic sequence can be found here.

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