Question

set of no. of multiples of 6 between 20 and 300 ​

Answer 1

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.