which term of the arithmetic sequence 5,9,13,17,...is 401
Answers
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
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 term of an AP
=
where,
is the first term of the AP
is the number of terms in the series
is the common difference
Now, we have been given the following information:
Putting these value in the formula to calculate the 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.