Question

(Example: (iv) Find the sum of an A.P. of nineteen terms whose middle term is 10.​

Answer 1

Answer: 190    mark as brainliest

Step-by-step explanation:

middle term is 10  and no. of terms, n = 19  

i,e t 10 = 10

or, a + 9d = 10  -------eqn i

Now,

Sum of terms, S  = n/2[2a + (n − 1) × d]

= 19 /2 [ 2a+ 18 d]

= (19 /2) * 2 [ a + 9d ]

= 19 * 10 -----> from eqn i

= 190

Answer 2

The sum of an A.P. of nineteen terms whose middle term is 10 is 190.

Given data:

There are 19 terms in an A.P, so n = 19.

It is given that the middle term of the series is 10.

Now we have to find out the middle term, as the value of n is 19. It is an odd number

So the middle is calculated as, n+1/2= 19+1/2=20/2=10.

The 10th term is the middle term, that is T₁₀=10 ----(1).

The general term formula for arithmetic progression is a+(n-1)d.

T₁₀=a+9d

10=a+9d  (from equation 1) -----(2)

Sum of the terms of the series is given by

Sn=$\frac{n}{2}$(2a+(n−1)d)

Substituting the value of n we have, we get

S19=$\frac{19}{2}$(2a+(19−1)d)

S19=$\frac{19}{2}$(2a+18d)

S19=19(a+9d)

S19=19(10) (from equation 2)

S19=190.

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