Question

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An ap has 27 terms the sum of the middle term and the two terms adjacent one each side of it is 177 if sum of the last term last three terms is 321, find the first three of an ap​.

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Answer 1

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Answer 2

Answer:

here is the best answer below

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