find the sum of 25th term of the list of numbers whose nth term is an=5+2n​

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find the sum of 25th term of the list of numbers whose nth term is an=5+2n​

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Liliana 4 weeks 2021-10-29T20:59:30+00:00 2 Answers 0 views 0

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    0
    2021-10-29T21:00:31+00:00

    Answer:

    Given :t_n = 5 – 2nt

    n

    =5−2n

    To Find: Find the sum of first 25 terms of an AP whose nth term is given by tn = 5- 2n

    Solution:

    t_n = 5 – 2nt

    n

    =5-2n

    Put n =1

    t_1 = 2 – 3(1)t

    1

    =2−3(1)

    t_1 = -1t

    1

    =−1

    put n =2

    t_2 = 2 – 3(2)t

    2

    =2−3(2)

    t_2= -4t

    2

    =−4

    put n =3

    t_3 = 2 – 3(3)t

    3

    =2−3(3)

    t_3= -7t

    3

    =−7

    So, A.P. become s: -1 , -4 , -7, ……..

    So, first term =a= -1

    Common difference d = -4-(-1)=-7-(-4)= -3

    Formula of sum of first n terms : \frac{n}{2}(2a+(n-1)d)

    2

    n

    (2a+(n−1)d)

    Put n =25

    \frac{25}{2}(2(-1)+(25-1)(-3))

    2

    25

    (2(−1)+(25−1)(−3))

    \frac{25}{2}(-2-72)

    2

    25

    (−2−72)

    \frac{25}{2}(-74)

    2

    25

    (−74)

    -925−925

    Hence the sum of first 25 terms of an AP is -925

    0
    2021-10-29T21:01:10+00:00

    Step-by-step explanation:

    an=5+2n

    for n=1

    a1=5+2(1)

    =5+2

    =7

    hence the first term is 7

    for n=2

    a2=5+2(2)

    =5+4

    =9

    hence second term is 9

    d=a2-a1

    =9-7

    =2

    hence the common difference is 2

    Sn=n/2(2a+d(n-1))

    S25=25/2(2×7+2(25-1))

    =25/2(14+2(24))

    =25/2(14+48)

    =25/2(62)

    =25×31

    =775

    hence the sum of the first 25 terms is 775

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14:4+1-6*5-7*14:3+5 = ? ( )