Math, asked by alend6622, 3 months ago

how many term of an ap -6,-11/2,5needed togive the sum-25

Answers

Answered by kanishk555791
0

Answer:

5 terms will be required

Answered by susobhanakhuli8537
0

Answer:

20

Step-by-step explanation:

Let, the terms needed to give the sum -25 is X

∴ The 1st term of the AP series is = - 6  & the common difference is

= (\frac{-11}{2} - (-6)) = \frac{1}{2}

∴ According to the formula,

                  the sum of the X terms are = \frac{X}{2} * (2 * (- 6) + (X - 1) * \frac{1}{2}) = -25

                                                               => \frac{X}{2} * (-12 +  \frac{X}{2} - \frac{1}{2}) = -25

                                              => \frac{X}{2}* \frac{-24+X-1}{2} = -25

                                             => X (-25 + X) = -25 * 4

                                         => -25X + X² = -100

=> X² - 25X + 100 = 0

=> X² - 20X - 5X + 100 = 0

=> X * (X - 20) - 5 * (X - 20) = 0

=> (X - 5) * (X - 20) = 0

∴ X = 5 or, X = 20

∵ X ≠ 5

∴ X = 20

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