Question

on find the number of terms in each term AP
.
1
7, 13, 19..., 205​

Answer 1

Number of terms = 34

Given

An AP

7 , 13 , 19 , ... , 205

To Find

Number of terms

Knowledge Required

$\bf \pink{\bigstar\ \; a_n=a+(n-1)d}$

Solution

Given ,

First term , a = 7

Common difference , d = 13 - 7 = 6

Last term , aₙ = 205

$\to \rm a_n=a+(n-1)d\\\\\to \rm 205=7+(n-1)6\\\\\to \rm 205=7+6n-6\\\\\to \rm 205=6n+1\\\\\to \rm 6n=204\\\\\to \bf \green{n=34\ \; \bigstar}$

So , Number of terms = 34

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

The

${n}^{th}$term of an Arithmetic progression is

$= a \: + (n - 1)d$

Where First term = a

Common Difference = d

TO DETERMINE

The number of terms in the Arithmetic Progression

$1, 7, 13, 19..., 205$

CALCULATION

$\sf{First \: term \: = a = 1}$

$\sf{Common \: Difference \: = d = 7 - 1 = 6}$

Let the number of terms = n

So

$a + (n - 1)d \: = 205$

$\implies \: 1 + (n - 1) \times 6= 205$

$\implies \: (n - 1) \times 6= 204$

$\implies \: (n - 1) = 34$

$\implies \:n= 35$

RESULT

The number of terms = 35