Given the recursive formula for an arithmetic sequence find the common difference and the 52nd term

              Common difference(d)                  

(21)                   -10                                          -548

(22)                   -7                                          -323

(23)                    10                                           547

(24)                   -100                                       -5118

Step-by-step explanation:

Let the common difference be denoted by 'd'.

Also the nth difference of an arithmetic sequence is given by:

(21)

We are given a recursive formula as:

The first term is given by:

The common difference for an arithmetic sequence is given by:

Hence, here we have the common difference as:

The nth term of an arithmetic sequence is given by:

Here and .

Hence,

Hence,

(22)

The common difference for an arithmetic sequence is given by:

Hence, here we have the common difference as:

Here and .

Hence,

Hence,

(23)

The common difference for an arithmetic sequence is given by:

Hence, here we have the common difference as:

Here and .

Hence,

Hence,

(24)

The common difference for an arithmetic sequence is given by:

Hence, here we have the common difference as:

Here and .

Hence,

Hence,

69

step-by-step explanation:

7 ft 6 in means 7 1/2, because 6 in is 1/2 of a foot. 7 ft 8 in means 7 2/3 because 8 in is 2/3 of a foot. 23/3 = 7 2/3. 15/2 = 7 1/2.

23/3   *   15/2   = 57 1/2

step-by-step explanation: