Question

how many terms of an ap :-15,-13,-11. ........ are needed to maike sum -55 ?

Answer 1

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Answer 2

Step-by-step explanation:

Formula for finding out the sum of A.P is

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

A.T.Q,

a= -15

d= 2

Sn= -55

Putting these values in the formula:

=》-55 = n/2 [ 2× (-15) + (n-1) 2]

=》-55 = n/2 [ -30 + 2n-2]

=》-55 =n/2 [ 2n- 32]

=》-55 × 2 = 2n^2 - 32n

=》-110 = 2n^2 - 32n

=》2n^2 -32n + 110 = 0

=》2n^2 -10n - 22n + 110 = 0

=》2n ( n -5 ) - 22 ( n- 5) =0

=》(2n - 22) (n - 5) = 0

=》 2n-22 = 0 , (n - 5)=0

=》 n= 22/ 2 , n = 5

Therefore n= 11 or 5

so, number of terms required is 11 or 5