6th term of ap is -10 and 10th term is -26 determine 15th term of ap

Question

6th term of ap is -10 and 10th term is -26 determine 15th term of ap

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Madelyn 1 month 2021-08-13T08:54:08+00:00 2 Answers 0 views 0

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    0
    2021-08-13T08:55:18+00:00

    Answer:

    -46

    Step-by-step explanation:

    we can write 6th term as A+5D=-10(1) AND 10th term as A=9D=-26.(2)

    NOW SUBTRACT THE BOTH EQUATIONS:-

    A+5D=-10-(1)

    A+9D=-26-(2)

    so,-4D=16 hence d=-4

    A+5(-4)=-10

    A-20=-10

    A=-10+20

    ∴A=10

    ∴SO, WE CAN WRITE 15TH TERM AS A+14D=10+14(-4)=10-56=-46

    hence the value of the 15th term is -46

    HOPE IT WILL HELP YOU

    0
    2021-08-13T08:56:03+00:00

    \bf\large\underline\green{Solution:-}

    \sf{{a_n} = a+ (n - 1)d}

    \sf{{a_6} = a+ (6 - 1)d \:and\: a - 10 = a +(10 - 1) d}

    \sf{{a_6} = a + 5d \: \:and \:  \:{a}_{10}= a + 9d}

    => a + 5d = -10 ⠀⠀⠀⠀ …………….(i)

    => a + 9d = -26 ⠀⠀⠀⠀ ……………..(ii)

    On subtracting (i) from (i), we get

    => 4d = -16

    => d = -4

    On substituting d= -4 in (i), we get

    => a + 5 x (-4) – 10

    => a = 10

    Thus, a = 10 and d = -4

    \sf{15^{th}\: \:term = {a}_{15} = a + (15 - 1) d}

    \sf{=\:(a + 14d) = [10 +14\:x\:(-4)]}

    \sf{= (10 - 56)}

    \sf\boxed{\red{\underline{= -46}}}

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