Question

The first term of an arithmetic sequence is 1/2 and T22 = 10. Find Tn​

Answer 1

`\text{First term, a} = \frac 12\\\\T_(22) = 10\\\\\implies a + (22-1) d = 10\\\\\implies \frac 12 + 21d =10 \\\\\\\implies \frac{1+42d}2 =10\\\\\implies 1+ 42 d = 20 \\\\\implies 42d = 19 \implies d = (19)/(42)\\\\\text{nth term ,}~\\ T_n =a +(n- 1)d = \frac 12 + (n-1)(19)/(42)=\frac 12 \left[1 + (n-1)(19)/(21)\right]`