If the sum of nth term of the series can be calculated by using S= 4n²+6n. What is the first term of the AP?​

Question

If the sum of nth term of the series can be calculated by using S= 4n²+6n. What is the first term
of the AP?​

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Serenity 1 month 2021-08-18T04:02:33+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-08-18T04:04:27+00:00

    We have,

    S

    n

    =4n−n

    2

    Taking n=1 and we get,

    S

    1

    =4×1−1

    2

    =4−1

    S

    1

    =3

    So, the sum of fristr term of an A.P. is 3.

    But, sum of first term will be the first term.

    So, first term a=3.

    Now, taking n=2 and we get,

    S

    n

    =4n−n

    2

    S

    2

    =4×2−2

    2

    S

    2

    =4

    Then, sum of first 2 terms is 4.

    Now, finding Secondterm.

    Then,

    According to given question,

    Firstterm+Secondterm=4

    3+a

    2

    =4

    a

    2

    =1

    Hence the A.P.is

    First term a=3

    Common difference

    d=Secondterm-firstterm

    d=1-3

    =-2

    The third term of

    a

    3

    =a+2d

    a

    3

    =3+2×(−2)

    a

    3

    =−1

    Similarly, 10

    th

    term

    a

    10

    =a+9d

    =3+9(−2)

    =3−18

    =−15

    Then,

    n

    th

    termis

    a

    n

    =a+(n−1)d

    a

    n

    =3+(n−1)(−2)

    a

    n

    =3−2n+2

    a

    n

    =5−2n

    Hence, this is the answer.

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