Question

Write the nth term of the following sequence in terms of the first term of the sequence.. 1, 8, 15, 22, . . .

Answer 1

Answer:

The Given sequence is : 1,8,15,22,.....

As, difference of two consecutive terms is same,which is =7, so it is an arithmetic progression.

First term = a=1

Common difference(d) = Second term - first term = Third term - Second term

                                  = 8 -1 or 15-8

                                   = 7

nth term of the Sequence$(a_{n})$

                                     = a + (n-1)× d

                                    = 1 + (n-1)× 7

                                   = 1 + 7 n - 7

                                  = 7 n -6

Answer 2

$1,\ 8,\ 15,\ 22,...\ is\ an\ arithmetic\ sequence:\\\\8-1=7\\15-8=7\\22-15=7\\\\a_1=1;\ d=7\\\\a_n=a_1+(n-1)d\\\\subtitute\\\\a_n=1+(n-1)\cdot7=1+7n-7=7n-6\\\\Answer:\boxed{a_n=7n-6}$