Question

how many terms of the AP 7,11,15 etc be taken to get the sum 250 ( with steps)​

Answer 1

Answer:

10

Step-by-step explanation:

7,11,15.... are in A.P.

a=7   d=11-7=4 Sn=250 n=?

Sn=n/2(2a+(n-1)d)

500=n(14+4n-4)

500=14n+4n^2-4n

4n^2+10n-500=0

n=− 25 /2 or 10

as n cannot be negative

n=10

Answer 2

Given :-

Arithmetic progession ;

7 , 11 , 15 . . . . . . . .

Required to find :-

• Sum of how many terms of the AP is 250

Formula used :-

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

Solution :-

Given information :-

AP = 7 , 11 , 15 . . . . . . . .

we need to find the sum of how many terms of the AP is 250

Consider the given information

AP = 7 , 11 , 15 . . . . .

• First term ( a ) = 7

Common difference = ( 2nd term - 1st term ) = ( 3rd term - 2nd term )

=> ( 7 - 11 ) = ( 15 - 11 )

=> ( 4 ) = ( 4 )

• Common difference ( d ) = 4

Using the formula ;

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

Here,

• a = first term

• d = common difference

• n = the term number till which you want to find the sum

$\longrightarrow\rm{ {S}_{nth} = 250 }$

$\longrightarrow\rm{ 250 = 2( 7 ) + ( n - 1 ) 4 }$

$\longrightarrow\rm{ 250 = 14 + ( n - 1 ) 4 }$

$\longrightarrow\rm{ 250 = 14 + 4n - 4 }$

$\longrightarrow\rm{ 250 = 10 + 4n }$

$\longrightarrow\rm{ 250 - 10 = 4n }$

$\longrightarrow\rm{ 240 = 4n }$

$\longrightarrow\rm{ 4n = 240 }$

$\longrightarrow\rm{ n = \dfrac{ 240 }{ 4} }$

$\longrightarrow\rm{ n = 60 }$

• Number of terms = 60

Therefore ,

Sum of first 60 terms of the AP is 250

Additional Information :-

Formula to find the nth term of the arithmetic progession is ;

$\large{\leadsto{\boxed{\sf{\bf{ {a}_{nth} = a + ( n - 1 ) d }}}}}$

The simplified formula to find the sum of the nth term ( when last term is given ) is ;

$\large{\dagger{\boxed{\rm{ {S}_{nth} = \dfrac{ n}{ 2 } [ First \; term + Last \; term ]}}}}$

Note :-

This formula is used reduce the calculations . In order to use this formula you need to know the last term till which you want to find the sum .