JAMB Mathematics 2022 Paper

only solution HTML. Need solve independently. AP 10th term=32 first a=3/2. T10=a+9d=32 => 9d=32-1.5=30.5=61/2 => d=61/18. T4=a+3d=3/2+183/18? 3*61/18=183/18=61/6=10.1667, +1.5=11.6667=35/3? 35/3=11.6667 yes. Option A. Need format with Concept, Explanation, Answer. Include formulas in LaTeX. Must use raw HTML, after each step. Concise. Output only HTML.Concept:Use the formula for the $n$th term of an arithmetic progression: $T_n = a + (n-1)d$.Explanation:Given: first term $a = \frac{3}{2}$ and 10th term $T_{10} = 32$.Substitute into the formula:$$32 = \frac{3}{2} + (10-1)d$$$$32 = \frac{3}{2} + 9d$$$$9d = 32 - \frac{3}{2}$$$$9d = \frac{61}{2}$$$$d = \frac{61}{18}$$Now find the 4th term:$$T_4 = a + 3d$$$$T_4 = \frac{3}{2} + 3\left(\frac{61}{18}\right)$$$$T_4 = \frac{3}{2} + \frac{61}{6}$$$$T_4 = \frac{9 + 61}{6} = \frac{70}{6} = \frac{35}{3}$$Answer:The 4th term is $\frac{35}{3}$, which is option A.