Question

the term to term rule for the sequence​

Answer 1

Answer:-

Given:

$U _{n + 1} = U_{n} + 2 \\ \\ <strong>U_{3} = - 4</strong> \\ \\ =>\: U_{2 + 1} = - 4 \\ \\ => \: U_{2} + 2 = - 4 \\ \\ <strong> </strong><strong>=</strong><strong>></strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>U_{2} = - 6</strong> \\ \\ U_{1 } + 2 = - 6\\\\=> \: U_{1} = - 6 - 2\\ \\ => \: <strong>U_{1} = -</strong> <strong>8</strong><strong>\</strong><strong>\</strong><strong>\</strong><strong>\</strong> U_{4} = U_{3} + 2\\ \\ => \: U_{4} = - 4 + 2\\\\<strong>=</strong><strong>></strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>U_{4} = - 2</strong> \\ \\ U_{5} = U_{4} + 2 \\ \\ => \: U_{5} = - 2 + 2 \\\\<strong>=</strong><strong>></strong><strong> </strong><strong>\</strong><strong>:</strong><strong>U_{5}= 0</strong>$

Hence, the first five terms of the given sequence are - 8, - 6 , - 4 , - 2 , 0.