Math, asked by anugyasoni, 1 year ago

how many terms of the AP 17,15,13,11,......... must be added to get the sum 72?explain the double answer.
PLZZZZ NO SPAMS ....
ONLY APPROPRIATE EXPALANATION!!!!!!!!!!!!

Answers

Answered by Anonymous
16


ѕolυтιon

a = 17

d = 15- 17 =-2

n=?

ѕn=72

==>72= n/2(2*17 + (n-1)*-2)

==>144 = n(34-2n+2)

==>144= 36n - 2n^2

==>n^2-18n+72=0

==>n^2-12n-6n+72

==>n(n-12)-6(n-12)

==>n=12 oғ n=6 anѕ......✳️✳️

anugyasoni: what is the explain the double anser
Anonymous: вecaυѕe ιт ιѕ qυadraтιc eqυaтιon ѕo
anugyasoni: what?????
Answered by Swarup1998
20
♧♧HERE IS YOUR ANSWER♧♧

The AP is

17, 15, 13, 11, ...

So, first term, a = 17,

second term = 15.

Then, common difference,

d = 15 - 17 = - 2.

Let us consider the AP contains n number of terms.

Sum of an AP series = 72

=> (n/2)[2a + (n-1)d] = 72

=> (n/2)[2×17 + (n-1)×(-2)] = 72

=> (n/2)[34 - 2n + 2] = 72

=> (n/2)(36 - 2n) = 72

=> n(18 - n) = 72

=> n² - 18n + 72 = 0

=> n² - 12n - 6n + 72 = 0

=> n(n - 12) - 6(n - 12) = 0

=> (n - 12)(n - 6) = 0

So, n = 12, 6.

Here, n = 6 is the required number of terms.

Since the AP is having first term 17 (positive) and common difference (-2) (negative), there are two values of n.

The sum of the last six terms (when n = 12) is 0 indeed.

So, only (6 - 4) = 2 or (12 - 4) = 8 terms need to be added.

♧♧HOPE THIS HELPS YOU♧♧
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