Question

What is the sum of the first 11 terms of an arithmetic progression if the 4th term is 11 and the 7th term is -4?

Answer 1

heya !!

here's your solution :-

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Given that ,

■ 4th term of an A.P. = 11

==》a + ( n - 1 ) d = 11

==》a + ( 4 - 1 ) d = 11

==》a + 3d = 11 ..................( 1 )

■ 7th term of an A.P. = - 4

==》a + ( n - 1 ) d = - 4

==》a + ( 7 - 1 ) d = - 4

==》a + 6d = - 4 ..................( 2 )

On subtracting :-

=》( a + 3d = 11 ) - ( a + 6d = - 4 )

=》( a - a + 3d - 6d ) = 11 - ( - 4 )

=》( - 3d = 15 )

=》d = - 5

☆ Hence , differences is - 5. Put the value of 5 on eq. ( 1 ) :-

=》a + 3d = 11

=》a + 3 ( - 5 ) = 11

=》a - 15 = 11

=》 a = 11 + 15

=》a = 26

☆ Hence , first term is 26.

So , the sum of first 11th term of an Arithmetic progress will be :-

■ Sn = n / 2 [ 2a + ( n - 1 ) d

=》S11 = 11 / 2 [ 2 * 26 + ( 11 - 1 ) - 5

=》S11 = ( 11 * 26 ) + ( 10 * - 5 )

=》S11 = 286 + ( - 50 )

=》 S11 = 236

☆ Hence , the sum of the 11th term of an Arithmetic progress is 236.
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hope it helps !!

thanks for asking :)

☆ be brainly ☆

Answer 2

Answer:

Step-by-step explanation: