Question

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!!!!!!!!!!!!

Answer 1

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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......✳️✳️

Answer 2

♧♧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♧♧