Maths...8+13+18+......is an arithmetic series.......?

Question

1. show that T10 the tenth term of the series is 53......
2. Find the expression for Sn the sum of the nth terms......
3.show that 3S3 - 2 = 5T4, where S3 is the sum of the first 3 terms
please show work. thanks very much. and thanks again for answerin the last Q..........rob

Answer 1

The formula for calculating T[n] in an arithmetic series is

T[n] = a + (n - 1)d

Since the first term a = 8, and the difference is equal to 5, then

T[10] = 8 + (10 - 1)(5)
T[10] = 8 + (9)(5)
T[10] = 8 + 45
T[10] = 53

Answer 2

This is an arithmetic progression with first term,a=8, common difference d=5.
Tn, the nth term is a+ (n-1)*d=8+5*(n-1) = 3+5*n

1. T10= 3+ 5*10 = 53

2. Sn= (n/2)*(2*a +(n-1)*d)
= (n/2)*(16+5*n-5) =(n/2)*(11+5*n)
=(1/2)*(5*n^2+11*n)

3. Using above formula: S3=(1/2)*(45+33) = 39

Therefore, LHS= 3*39-2 = 115
RHS = 5*T4= 5(3+5*4) =5*23 = 115
Hence LHS=RHS

Hope this helps!