Math, asked by dhillontaranjot01, 4 months ago

How
many
terms of the
AP 24,21 must be taken
that the sum is 78?

Answers

Answered by dayanidhisharma19
0

Answer:

No. of term to be taken eithor 4 and 13 to get sum = 78.

Step-by-step Explanations :

Given : AP = 24,21..

Sn = 78

To find : n = ?

AP = 24, 21 , 18 ..

So,

First term of AP = (a) = 24, common difference (d) = (21 - 24) = -3

Let n no. of terms to be taken, So that sum = 78

So, sum of n terms of the AP,

Sn = n/2 × [2a + (n-1)d]

Substituting the given value in above formula we get,

= n/2 × (2 x 24 + (n-1) × (-3)

∴ n/2 × [48 + (n - 1) x (-3)] = 78

=> (48 +3 - 3n)n = 78 x 2

=> (51 - 3n)n = 78 x 2

=> (17 - n)n = 26 x 2 .. ( dividing by 3 )

=> n² - 17n = 52

=> n² - 17n + 52 = 0

=> n² - 13n - 4n + 52 = 0

=> n(n - 13) - 4(n - 13) = 0

=> (n - 13)(n - 4) = 0

∴ n = 4 and n = 13 (since, some terms be negative after zero)

Hence, no. of term to be taken eithor 4 and 13 to get sum = 78.

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