th 1. The nth term of an A.P. is given by an = 3 + 4n. The common difference is (a) 7 (b)3 (c) 4 (d) 1​

Question

th
1.
The nth term of an A.P. is given by an = 3 + 4n. The common difference is
(a) 7
(b)3
(c) 4
(d) 1​

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Ayla 3 weeks 2021-11-19T13:49:11+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-11-19T13:50:24+00:00

     \red{ \underline{answer}} \\  \\ \implies {common \:  \: difference \:  \:  =  \:  \: 4} \\  \\ \implies  \green{ \underline{to \:  \: find}} \\  \\ \implies {common \:  \: difference} \\  \\ \implies \orange{ \underline{solution}} \\  \\ \implies {nth \:  \: terms \:  \: of \:  \: ap \:  } \\  \\ \implies {an = 3 + 4n \:  \: (given)} \\  \\ \implies {put \:  \: n \:  = 1 = 7} \\  \\ \implies {put \:  \: n \:  = 2 = 3 + 8 = 11} \\  \\ \implies {put \:  \: n \:  = 3 = 3 + 12 = 15} \\  \\ \implies {put \:  \: n \:  = 4  =3 + 16 = 19 } \\  \\ \implies {ap \:  \:  =  \:  \: 7 + 11 + 15 + 19....... \: n \: terms} \\  \\ \implies {first \:  \: term \:  \: =  a \:   = 7} \\  \\ \implies {common \:  \: difference \:  = d = 11  - 7 = 4} \\  \\ \implies  \pink{ \underline{verification}} \\  \\ \implies { \boxed{an \:  =  \: a \:  + (n - 1)d}} \\  \\ \implies {an \:   = 7 + (n - 1)4} \\  \\ \implies {7 + 4n - 4} \\  \\ \implies {3 + 4n} \\  \\ \implies  \green \therefore \green{ \boxed{verified}} \\  \\ \implies  \orange{ \underline{related \:  \: formula}} \\  \\ \implies { \boxed{an \:  = a + (n - 1)d}} \\  \\ \implies { \boxed{sn \:  =  \frac{n}{2}(2a + (n - 1)d }}

    0
    2021-11-19T13:50:29+00:00

    QUESTION:

    The nth term of an A.P. is given by an = 3 + 4n. The common difference is

    (a) 7

    (b)3

    (c) 4

    (d) 1

    ANSWER:

    The nth term of an AP is given by;

    an = 3 + 4n

    If we put the value 1 that is a1 then we will get the first term;

    a(1) = 3 + 4 \times 1 \\ a(1) = 3 + 4 \\ a(1) = 7

    \huge\orange{first \: term = 7}

    If we put the value 2 that is a2 then we will get the second term ;

    a(2) =  3 + 4 \times 2 \\ a(2) = 3 + 8 \\ a(2) = 11

    \huge\pink {second \: term = 11}

    now,

    we know that;

    \blue {second \: term - first \: term = common \: differnce}

    \red{a2 - a1 = d}

    so,

    d = 11 - 7 \\ d = 4

    \huge\green {common \: differnce = 4}

    your answer is option c ✔✔.

    plz Mark as brainliest.

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