A maths question on series and sequences.?

Question

A sequence satisfies Tn = 1/2 (Tn-1 + Tn+1), with T1 = 3 and T2 = 7. Find T3 and T4.

The number after the T means the nth term. Also Tn-1 means the term before the nth term and Tn+1 means the term after the nth term.. i just cant type it up properly.

Answer 1

The series is 3, 7, 11, 15 etc where T1 is 3, T2 is 7, T3 is 11 and T4 is 15. The sequence Tn=1/2(Tn-1 + Tn+1) is finding the average(mean) of the 2 numbers. So mean of 3 and 11 is 7 and the mean of 7 and 15 is 11.
To get your answers solve T2=1/2(T1 + T3) where T2 is 7 and T1 is 3. So 7=1/2(3+ T3). Hence 14=3+T3, Then 11=T3.
Now solve T3=1/2(T2+T4). So 11=1/2(7+T4). Hence 22=7+T4. Then 15=T4. Done!