Question

The sum of the series 2,5,8,11,...... is 60100. find the number of terms.​

Answer 1

Answer:

a=2

d=5-2=8-5=3

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

60100=n/2(2×2+(n-1)3)

60100×2=n(4-3+3n)

60100*2=n+3n^2

3n^2+n-120200=0

3n^2+601n-600n-120200=0

n(3n-601)-200(3n-601)=0

(3n-604)(n-200)=0

n=200

Answer =no. of terms is 200

Answer 2

Answer:

Step-by-step explanation:

2,5,8,11,..... is forming an AP

hence sum for an AP

\frac{n}{2} (2a + (n - 1)d) \\ d = 3 \\ a = 2 \\we \: have \: to \: find \: n \\ \frac{n}{2} (4 + 3n - 3) = 60100 \\ \\ n + 3 {n}^{2} - 120200 = 0 \\ solving \: this \: you \: will \: get \\ n = 200