Question

How many multiples of 6 lie between 20 and 300​

Answer 1

Answer:

answer is 46

first step check whether it ends with 300 or not

seconds step if it's end with 300 then it starts with 20 or not

third step find the difference of the numbers you found

such as -:

6×50= 300

6×4 =24

then 50-4= 46

Answer 2

GIVEN :-

• common differnce (d) = 6

• first term (a) = 24
• last term (an) = 300

TO FIND :-

• number of terms in ap

SOLUTION :-

as we know that according to formula of Ap

$\implies \boxed{ \rm{ a_{n} = a + (n - 1)d}}$

now put the values in given formula

$\implies \rm{300 = 24+ (n - 1)(6)}$

$\implies \rm{300 - 24 = (n - 1)(6)}$

$\implies \rm{276 = (n - 1)(6)}$

$\implies \rm{ \dfrac{276}{6} = (n - 1)}$

$\implies \rm{46 = n - 1}$

$\implies \rm{46 + 1 = n }$

$\implies \rm{ n =47 }$

$\implies \boxed{ \boxed{\rm{number \: of \: terms = 47}}}$

OTHER INFORMATION :-

Sequences, Series and Progressions

• A sequence is a finite or infinite list of numbers following a certain pattern. For example: 1, 2, 3, 4, 5… is the sequence, which is infinite.sequence of natural numbers.

• A series is the sum of the elements in the corresponding sequence. For example: 1+2+3+4+5….is the series of natural numbers. Each number in a sequence or a series is called a term.

• A progression is a sequence in which the general term can be can be expressed using a mathematical formula.

Arithmetic Progression

• An arithmetic progression (A.P) is a progression in which the difference between two consecutive terms is constant.

• Example: 2, 5, 8, 11, 14…. is an arithmetic progression.

Common Difference

• The difference between two consecutive terms in an AP, (which is constant) is the “common difference“(d) of an A.P. In the progression: 2, 5, 8, 11, 14 …the common difference is 3.

• As it is the difference between any two consecutive terms, for any A.P, if the common difference is:

• positive, the AP is increasing.

• zero, the AP is constant.

• negative, the A.P is decreasing.

• Finite and Infinite AP

• A finite AP is an A.P in which the number of terms is finite. For example: the A.P: 2, 5, 8……32, 35, 38

• An infinite A.P is an A.P in which the number of terms is infinite. For example: 2, 5, 8, 11…..

• A finite A.P will have the last term, whereas an infinite A.P won’t.