Question

The Terms in two positions of some Arithmetic sequence are given below write the first term of each:3rd term=2 5th term=3

Answer 1

Answer:

$third \: term =2 \\ a_3 = 2 \\ a + 2d = 2 - (i) \\ fifth \: term = 3 \\ a_5 = 3 \\ a + 4d = 3 - (ii) \\ \blue{\mathfrak{\underline{\large{Subtract \: equation \: (i) \: in \: (ii)}}}:} \\ a + 4d = 3 \\ a + 2d = 2 \\ - \: \: \: \: - \: \: \: \: \: \: \: \: \: - \: \: \: \: \: \: \: \: \\ - - - - - - - \\ \: \: \: \: \: \: \: \: 2d = 1 \\ \boxed{d = \frac{1}{2} } \\\blue{\mathfrak{\underline{\large{put \: the \: value \: of \: 'd' \: in \: {eq}^{n} \: (i) }}}:} \\ a + 2 \times \frac{1}{2} = 2 \\ \boxed{a = 1} \\ hence, \: first \: term = a =⟩ 1 \\ \\ \red{\mathfrak{ \large{\underline{{Hope \: It \: Helps \: You}}}}} \\ \blue{\mathfrak{ \large{\underline{{Mark \: Me \: Brainliest}}}}}$