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FIND THE SUM OF FRIST 17 TERMS OF AN A.P WHOSE 4TH AND 9TH TERM ARE -15 AND -30 RESPECTIVELY

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let the first term is a and difference is d

now ...

=>a(4)=a+(4-1)d=-15

a+3d=-15..........[I]

=>>and .........

=>>a(9)=a+(9-1)d=-30

=>>a+8d=-30..........[II]

from EQUATIONS (I) and (ii)

=>>-15-3d=-8d-30

=>>5d=-15

=>>d=-3

therefore...a=-15-3(-3)=-6

now the SUM of 17 terms is....

s(17) = \frac{17[( 2 \times ( - 6) + (17 - 1)( - 3)]}{2} \\ = > s(17) = \frac{17( - 12 - 48}{2} \\ = > s(17) = 17 \times ( - 30) = - 510

\underline{\large\mathcal\red{hope\: this \: helps \:you......}}


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