Question

ap has 27term the sum of the middle term of adject one of each side if sum are three terms is 321 find the ap ​

Answer 1

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Answer 2

Answer:

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Step-by-step explanation:

Let the 1st term = x1

for a.p., constant term added = n

.. we can write equation

x2 = x1 + n

x3 = x1 + 2n

xn = x1 + (n-1)n

- (1)

There are total 27 terms

The middle term will be 14th term

.. As per condition (1)

x13 + x14 + x15 = 177

MEa (0) Q 32 32

substituting from equation 1 we get,

x13 = x1 + 12n

x14 = x1 + 13n

x15 = x1 + 14n

:: x13 + x14 + x15 = (x1+12n) + (x1+13n)

+ (x1+14n) = 177

· (2)

::3x1 + 39n = 177.. (2)

For condition 2, sum of last three

terms = 321

x25 + x26 +x27 = 321

MEg (0) Q 32 32

-(X1 + 24n) + (x1 + 25n) + (x1 + 26n) =

321

: 3x1 + 75n = 321

.. 3x1 = 321 - 75n..

(3)

substituting the value in equation 2,

we get

(321 - 75n) + 39n = 177

. 321 - 177 = 75n - 39n

:: 144 = 36n

.. n = 4. (4)

Substituting in eqn (3),

3x1 + 75x 4 = 321

:: 3x1 + 300 = 321

:: 3x1 = 21

.. x1

= 7 . (5)

1st 3 terms of a.p.

x1 = 7

x2 = x1 + n = 7 + 4 = 11

x3 = x2 + 2 = 11+ 4 = 15

: x1

= 7x2 = 11, x 3 = 15