14 ? (-fifty 4 + 9i) i =5 nth term = 9i - fifty 4 nth term = 9(14)-fifty 4 an = seventy two an = 9i- fifty 4 a = 40 5 - fifty 4 a = - 9 -- first term worry-loose distinction= 9 an = a+ (n-a million)*d seventy two = -9 +9n - 9 seventy two = 9n - 18 9n = seventy two + 18 9n = ninety n = ninety/9 n = 10 Sum = n*(a+an)/2 Sum = 10*(-9+seventy two)/2 Sum = 5*(sixty 3) Sum = 315. . . .ans.
Comments
a5= 29, a8= 56.
the nth term of an Arithmetic Progression is given by,
an= a + (n-1)d
so, you have to calculate the value of a(first term) and d (common difference) here.
a5= a + 4d = 29 => a= 29 - 4d
a8= a + 7d = 56 => a= 56 - 7d
=> 29 - 4d = 56 - 7d
=> 3d = 27
=> d= 9.
a + 4d = 29
=> a + (4*9) = 29
=> a = -7.
sum of first 15 terms of the A.P:
S = 2a + (n-1)d
=> S = -14 + (15-1)*9
=> S = -14 + 126
=> S = 112.
An arithmetic series is one where the next number in the series is equal to the previous one plus a constant
e.g. 1, 3, 5, 7, 9 adding 2 each time
or 4,9,14,19,24 adding 5 each time
if we assume the series starts with x, and adds y each time then the first five terms are:
x, x+y, x+2y, x+3y, x+4y
so the fifth term is x+4y = 29
the eight term is x+?y = 56
from these two you can work out what x and y are, and then you can write down the first 15 terms and add them together
14 ? (-fifty 4 + 9i) i =5 nth term = 9i - fifty 4 nth term = 9(14)-fifty 4 an = seventy two an = 9i- fifty 4 a = 40 5 - fifty 4 a = - 9 -- first term worry-loose distinction= 9 an = a+ (n-a million)*d seventy two = -9 +9n - 9 seventy two = 9n - 18 9n = seventy two + 18 9n = ninety n = ninety/9 n = 10 Sum = n*(a+an)/2 Sum = 10*(-9+seventy two)/2 Sum = 5*(sixty 3) Sum = 315. . . .ans.
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