How many terms of the AP:24, 21, 18,… Must be taken so that their sum is 78?​

Question

How many terms of the AP:24, 21, 18,… Must be taken so that their sum is 78?​

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Raelynn 1 month 2021-08-19T07:42:14+00:00 1 Answer 0 views 0

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    2021-08-19T07:43:50+00:00

    Step-by-step explanation:

    Sum of n-th term of an AP , Sn = (n/2) [ 2a + (n-1) d ]

    Sn = 78 (given)

    A/Q,

    (n/2) [ 2 × 24 + ( n – 1 ) (-3) ] = 78

    => n [ 48 – 3n +3 ] = 78 × 2

    => n( 51 – 3n ) = 78 × 2

    => 3n( 17 – n) = 156

    => n( 17 – n) = 52

    =>

     { - n}^{2}  + 17n - 52 = 0

     {n}^{2}   - 17n + 52 = 0

    n = (17 + \sqrt{(289 - 208)} ) \div 2 \\ or \\ n = (17 -  \sqrt{(289 - 208)} ) \div 2

    n =( 17 - 9) \div 2 \\ or \\ n = (17 + 9) \div 2

    n = 4 \: or \: 13

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18:9+8+9*3-7:3-1*13 = ? ( )