Question

If the sum of the first 7 terms of an AP is 49 and that of 17terms is 289, find the sum of first n terms.

Plz answer me quickly

Answer 1

Hello,

Here is your Answer by Sujeet Yaduvanshi


Question:-) If the sum of the first 7 terms of an AP is 49 and that of 17terms is 289, find the sum of first n terms.





Answer:-)

Here,

Sum of the first n terms of an A.P, Sn = ( n / 2) [ 2a + ( n -1)d ]



Again,

Given:-) sum of the first 7 terms of an A.P is 49

S7 = 49.



So,

According to the formula:)

⇒ ( 7 / 2) [ 2a + 6d ] = 49

⇒ 2a + 6d = 14 

=)2(a+3d)=14

=)a+3d=14/2

=)a+3d=7 (1 €quation)


Now


Also given Sum of  first 7 terms of an A.P is = 289

S17 = 289

⇒ ( 17 / 2) [ 2a + 16d ] = 289.

⇒  [ 2a + 16d ] = 34.

⇒ a + 8d  = 17 -------(2)


Solving the equation:-)


a+3d=7
a+8d=17

By Elimination Method,

a+3d=7
a+8d=17

_________

5d=10

d=10/5

d=2

Now,

Putting the value of d in equation ,

a+3d=7


a+3(2)=7


a+6=7

a=7-6


a=1


NOW.

WE KNOW THAT FORMULA,



Sn = ( n / 2) [ 2a + ( n -1)d ]


Sn = ( n / 2) [ 2 + ( n -1)2 ]

Sn = ( n / 2) [ 2 + 2n - 2 ]


Sn=n/2 [2n)


Sn=2n^2/2


Cancel 2 And 2


then,


Sn = ( n^2)