Question

find algebraic form of following arithmetic sequence .2,7,12,...​

Answer 1

$\large \bold \orange{ \underline{answer \: = 5n - 3}}$

Step-by-step explanation:

$\bold{given \: } \\ ap = 2 + 7 + 12 + ....... + n \: terms \\ first \: \: term \: = 2 \\ common \: \: difference = a2 - a1 \\ 7 - 2 = 5 \\ \large \bold \green{ \underline{formula \: \: of \: \: n \: \: terms \: \: of \: \: an \: \: ap}} \\ an = a + (n - 1)d \\ an = 2 + (n - 1)5 \\ an = 2 + 5n - 5 \\ an = 5n - 3 \\ \large \blue{algebraic \: \: form \: \: of \: \: ap = \: \: 5n - 3} \\ \large \bold \orange{ \underline{extra \: \: information}} \\ an = 5n - 3 \\ put \: n = 1 = 2 \\ put \: n = 2 = 7 \\ put \: n = 3 = 12 \\ hence \: \: ap \: = 2 + 7 + 12 + ....... \\ \large \green{proved}$