The sum of the first 7 terms of an arithmetic progression is 140 and the sum of the next 7 terms of the same progression is 385 th

1 thought on “The sum of the first 7 terms of an arithmetic progression is 140 and the sum of the next 7 terms of the same progression is 385 th”

1. Answer:

   Step-by-step explanation:

   Solution :-

   Sum of first 7 terms () = 140

   Sum of next 7 terms = 385

   So, Sum of 14(7+7) terms ()= 140 + 385 = 525

   We know the formula of the sum of n terms of an A.P. i.e.,

   where,

   = Sum of n terms

   n = Number of terms

   a = First term

   d = difference of consecutive terms

   So,

   Now,

   We have the value of d and by subsituting the value of d in eq. i.), we will find the value of a.

   => 2a = 40 – 6d

   => 2a = 40 – 6 x 5

   => 2a = 40 – 30

   => 2a = 10

   => a =

   The first term of A.P. = a = 5

   The second term of A.P. = a + d= 5 + 5 = 10

   The third term of A.P. = a + 2d= 5 + 2 x 5 = 5 + 10 = 15

   The fourth term of A.P. = a + 3d = 5 + 3 x 5 = 5 + 15 = 20

   The fifth term of A.P. = a + 4d = 5 + 4 x 5 = 5 + 20 = 25

   The sixth term of A.P. = a + 5d= 5 + 5 x 5 = 5 + 25 = 30

   The seventh term of A.P. = a + 6d = 5 + 6 x 5 = 5 + 30 = 35

   The eighth term of A.P. = a + 7d = 5 + 7 x 5 = 5 + 35 = 40

   The ninth term of A.P. = a + 8d = 5 + 8 x 5 = 5 + 40 = 45

   The tenth term of A.P. = a + 9d = 5 + 9 x 5 = 5 + 45 = 50

   The eleventh term of A.P. = a + 10d = 5 + 10 x 5 = 5 + 50 = 550

   The twelfth term of A.P. = a + 11d = 5 + 11 x 5 = 5 + 55 = 60

   The thirteen term of A.P. = a + 12d = 5 + 12 x 5 = 5 + 60 = 65

   The fourteen term of A.P. = a + 13d = 5 + 13 x 5 = 5 + 65 = 75

   ∴ The A.P. –

   5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75.

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