Math, asked by marcelomichelle, 3 months ago

which term of the arithmetic sequence 5,9,13,17,...is 401​

Answers

Answered by rishkrith123
5

Answer:

The 100th term in the sequence 5, 9, 13, 17,.. is term 401.

Step-by-step explanation:

Given,

The arithmetic sequence:

5, 9, 13, 17,...

To find,

Which term of the arithmetic sequence 5, 9, 13, 17,...is 401​.

Concept,

For a given A.P sequence if the first term is 'a', the common difference is 'd', then the aₙth term is given by:

aₙ = a + (n - 1)d....(1)

Calculation,

Here in the given sequence:

5, 9, 13, 17,..

a = 5, d = 9 - 5 = 4, and aₙ = 401, n = n, substitute in equation (1)

401 = 5 + (n - 1)4

⇒ 396 = (n - 1)4

⇒ n - 1 = 99

⇒ n = 100

Therefore, the 100th term in the sequence 5, 9, 13, 17,.. is term 401.

#SPJ3

Answered by sureeshravi
0

Answer:

The 100th term of the arithmetic sequence is 401.

Step-by-step explanation:

Arithmetic progression:

Arithmetic Progression (AP) is a sequence or series of numbers in order, in which the difference between any two consecutive numbers is always constant, known as common difference (d).

Formula to calculate n^{th} term of an AP

= a+(n-1)d

where,

a is the first term of the AP

n is the number of terms in the series

d is the common difference

Now, we have been given the following information:
a= 5
d= 4
n^{th} term= 401
Putting these value in the formula to calculate the n^{th} term of an arithmetic sequence/progression

⇒ 401= 5+(n-1)4
⇒ 401= 5+4n-4
⇒ 401= 1+4n
⇒ 401-1= 4n
⇒ 400= 4n

∴n= 100

Thus, the 100th term of the arithmetic sequence 5,9,13,17,...... is 401.

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