insert four fractions between the numbers 1 and 3 so that the size numbers (including 1 and 3) constitute part of an arithmetic sequence.

Q: Insert three numbers between 5 and 80 so as to give five numbers in a geometric sequence.

A: Geometric sequence means ratio of two consecutive number is same.

Q: Find the first term or a1of an arithmetic sequence if a7=21 and a15= 45

A:

Q: Find the 24th term of the arithmetic sequence if the first term is 3 and common ratio is 2.

A: First term =  a1 = 3  Common ratio = r = 2  We have to find a24 .

Q: Find the 8th term of an arithmetic sequence with a1 = −2 and a15 = 68.

A: Using  a1 = −2 and a15 = 68 we find common difference d and use the term formula of AP.

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.