Question

Find 15th term of the Ap 4,7,10,13,.....

Answer 1

Question :-

Find the 15th term of the A.P 4,7,10,13 - - -

Answer :-

Given :-

Arthimetic progession = 4 , 7 , 10 , 13 , - - - -

Required to find :-

• 15th term in the Arthimetic progession / sequence ?

Formula used :-

$\Large{\boxed{\rm{{a}_{nth} = a + ( n - 1 ) d }}}$

Solution :-

Given arithmetic progession

a = 4 , 7 , 10 , 13 , - - - -

He asked us to find the 15th term in the sequence .

So,

a = 4, 7, 10 , 13 - - - -

Here,

First term ( a ) = 4

Similarly,

Common difference ( d ) = 3

So,

Using the formula,

$\Large{\boxed{\rm{{a}_{nth} = a + ( n - 1 ) d }}}$

Here,

• a = first term

• d = common difference

• n = the term which you want to find

So,

Here,

$\longrightarrow{\rm{ {a}_{nth} = {a}_{15}}}$

So,

$\longrightarrow{\rm{ {a}_{15} = a + ( n - 1 ) d }}$

Now substitute the respective values

$\longrightarrow{\rm{ {a}_{15} = 4 + ( 15 - 1 ) 3 }}$

$\longrightarrow{\rm{ {a}_{15} = 4 + (14) 3 }}$

$\longrightarrow{\rm{ {a}_{15} = 4 + 42 }}$

$\implies{\underline{\red{\tt{ {a}_{15} = 46 }}}}$

$\Large{\leadsto{\boxed{\mathsf{\therefore{15th \; term = 46 }}}}}$

Points to remember :-

1. To find any term of the given Arthimetic progession you should use the formula $\Large{\boxed{\rm{{a}_{nth} = a + ( n - 1 ) d }}}$

2. similarly, to find the sum of the arithmetic progession the formula is

$\tt{ {S}_{nth} = \dfrac{n}{2} [ First term + last term ] }$

The most accurate formula is ,

$\tt{ {S}_{nth} = \dfrac{n}{2} [ 2a + ( n - 1 ) d ] }$

Using these formulae we can solve many questions related to this arithmetic progession .

3. To find whether the given sequence is an arithmetic progession or not .

You should subtract the 2nd term and 1st term similarly, this value should be equal to value which we get by subtracting 3rd term and 2nd term

Then we can conclude that it is an arithmetic progession .