Arithmetic Sequence Formula

About Arithmetic Sequence Formula

The arithmetic sequence formula is used to calculate the nth term of an arithmetic progression. The common difference between any two subsequent terms in an arithmetic sequence remains constant. Any term in the arithmetic sequence can be found using the arithmetic sequence formula.

Arithmetic Sequence Formula

An Arithmetic sequence up to n terms looks like this: a, a+d, a+2d etc., where an is the 1st term, d is a common difference, and n is the number of terms. Using the arithmetic sequence formulae, find the first term, the number of terms, and the common difference. The nth term, sum, or common difference of an arithmetic series can be calculated using a variety of formulas.

a _n = a₁ +(n -1)d

s_n = n / 2[2a +(n -1)d]

d = a _n - a _n-1

s_n = n / 2[a₁ + a _n]

Where,

a_n = n ^thterm
a₁ = 1 ^stterm
n = noumber of term
s_n = Sum of n terms
a _n-1 = second last term

Formula2:- Now lets see the Arithmetic Sequence Formula is:-

an = al + (n -1)d

Where

an = nth term,
a1= first term, and
d is the common difference

The above formula is also known as the nth term formula of an arithmetic sequence

Formula2:- Sum of first n terms in an AP is given as,

s_n = n / 2[2a +(n -1)d]

Where

Sn = Sum of n terms,
a1= 1st term, and
d is the common in-difference between the successive terms

Formula3:- Formula for finding the common difference of an AP is given as,

d = a _n - a _n-1

where,

an = nth term,
an−1 = 2nd last term, and
d is the common difference in-between the successive terms

Formula4: Sum of first n terms of an AP using the first and the last terms are known is given as,

s_n = n / 2[a₁ + a _n]

where,

Sn = Sum of first n terms
an= last term, and
a1 = first term

Applications of Arithmetic Sequence Formula

Every day may be not every minute, but we employ the arithmetic sequence formula without even recognising it. Some real-life applications of the arithmetic sequence formula are listed below.

Cups, chairs, or a house of cards can all be stacked.
Arithmetic sequence is used to organise seats in a stadium or auditorium.
The second's hand, as well as the minutes and hour hands, move in Arithmetic Sequence on the clock.
The weeks in a month, as well as the years, follow the AP. Each leap year is calculated by multiplying the preceding leap year by four.
Every year, the number of candles blown on a birthday rises in arithmetic order.

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Arithmetic Sequence Formula

About Arithmetic Sequence Formula