Question

Find the 38th sequence of 8.5,16,23.5

Answer 1

Answer:

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Answer 2

Given Data:  8.5,16,23.5

To Find: 38th Sequence.

Solution:

• Arithmetic sequence is defined as the process where addition or subtraction of numbers occur to the next number.
• For example- 2, 4, 6, 8, 10 etc. In this arithmetic sequence 2 is added to the next numbers. So the difference is 2.
• Similarly in this sequence, Assign the values - $a_{1} = 8.5$;  $a_{2} = 16 ; a_{3} = 23.5$ .

                                 $a_{3} - a_{2} = 23.5-16= 7.5;\\a_{2} - a_{1} = 16 -8.5 =7.5;$

• The Difference in this sequence is, d= 7.5
• Calculating the 38th value using formula,

                                  $a_{n} = a_{1} +(n-1)d$. where n is 38.

                                  $a_{n}= 8.5 + (38-1)(7.5)\\ a_{n}= 8.5 + (37)(7.5)\\a_{n}= 8.5 + 277.5\\ a_{n}= 286$

• Hence the 38th value of the sequence is 286.