Question

Check whether 301 is a term of the list of numbers 5, 11, 17, 23, …………

Answer 1

$\bold\pink{AnswEr:-}$

$\large\bold{\underline{\sf{\red{GivEn:-}}}}$

AP :- 5 ;11 ;17 ;23;.......

Then,

★ First term (a) = 5

★ Common difference (d) = 11-5 = 6

$\large\bold{\underline{\sf{\red{To \; Find:-}}}}$

301 is a term of this AP or not.

Lets assume it is $n^{th}$ term of AP

So, $\sf a_n$ = 301

Now, $\sf a_n$ = a + (n - 1 ) d

$\implies$ Put values in formula :-

• 301 = 5 + ( n - 1 ) 6
• 301 = 5 + 6n - 6
• 301 = 6n - 1
• 302 = 6n

$\implies$ n = $\cancel {\dfrac{302}{6}}$

$\large\bold{\underline{\boxed{\sf{\pink{n = 50.3}}}}}$

$\large\bold{\underline{\sf{\red{Hence, \; it \; is \; not \; a \; term \; of \; AP}}}}$

___________________________________

Answer 2

Given :-

Arithmetic progession

5,11,17,23......

To find

Is 301 is the term of A.P or not

Now by forumula

$\bigstar{\boxed{\sf{a_n=a+(n-1)d}}}$

We have

First time (a)=5

last term $\sf a_n=301$

common difference (d)= $\sf a_2-a_1$

d = 11-5 = 6

numner of terms (n)=?

Now find the n

$\longmapsto\sf a_n=a+(n-1)d\\ \\ \longmapsto\sf 301=5+(n-1)6\\ \\ \longmapsto\sf 301-5=6n-6\\ \\ \longmapsto\sf 296+6=6n\\ \\ \longmapsto\sf 302=6n\\ \\ \longmapsto\sf n=\cancel{\dfrac{302}{6}}\\ \\ \longmapsto\sf n= \dfrac{151}{3}$

• 151 is not divisible by 3

So, 301 is not the term of A.P

Some formula related Ap

• To find last term

$\bullet {\boxed{\sf{a_n=a+(n-1)d}}}$

• To find the sum of given progession

$\bullet{\boxed{\sf{ S_n=\dfrac{n}{2}[2a+(n-1)d]}}}$

or

$\bullet {\boxed{\sf{S_n= \dfrac{n}{2}[a+a_n]}}}$