Question

Find the next term of the given sequence. 1.31, 2.54, 3.77, ... 4.90 5.00 5.10

Answer 1

It is A.P. with common difference = 2.54-1.31 = 1.23

So, next term would be 3.77+1.23 = 5.00

OPTION B IS YOUR ANSWER

Answer 2

Option B is correct.

the next term of the sequence is 5.00

Step-by-step explanation:

Arithmetic progression(A.P) is a sequence of numbers in which the consecutive terms are formed by adding a constant quantity with the preceding term.

Common difference(d) is the constant quantity stated in the above definition of arithmetic progression. it is given by;

`d=a_(n+1) - a_n` for all n∈N

Given sequence:- 1.31, 2.54 , 3.77 , ___ ;

we have;

`a_1 = 1.31` ,
`a_2= 2.54` and
`a_3 = 3.77`

First find the common difference;

`d =a_2 - a_1` =
`2.54-1.31 = 1.23`

or

d =
`=a_3-a_2 = 3.77-2.54 =1.23`

Therefore, by the definition of arithmetic progression,

the given sequence is Arithmetic progression

Now, to find the fourth term of the sequence, add constant quantity (d) to the third term;

`a_4 = 3.77+1.23 = 5.00`

Therefore, in the given sequence next term will be 5.00.