Question

the numbers of the terms of the series 10+29/3+28/3+9........will amount to 155 is
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Answer 1

in arithmetic progression

an = a1 + (n-1)d

s = n (a1 + an)/2

in this question,

a1 = 10

d = - 1/3

an will be

an= 10 -1/3 (n-1)

s= n (10 + 10 - 1/3 (n-1)) / 2 = 155

n (20 - 1/3 n + 1/3) = 310

20 n - 1/3 n2 + 1/3 n = 310

60 n - n2 + n = 930

n2 - 61 n + 930 = 0

(n - 30) (n -31) = 0

n = 30 or n = 31