The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
Correct Answer: 8
Solution and Explanation
Let the total number of terms be , and the first term is and common difference be .
.........(1)
If we take odd terms only it will also be an A.P. of terms with a common difference of ......(2).....(3)
Put the value of equation (3) in equation (2),
[Putting in equation (1)]
So,
So no. of terms .
Series
Hence, the correct answer is 8.
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Concepts Used:
Sequence and Series
Sequence: Sequence and Series is one of the most important concepts in Arithmetic. A sequence refers to the collection of elements that can be repeated in any sort.
Eg: a1,a2,a3, a4…….
Series: A series can be referred to as the sum of all the elements available in the sequence. One of the most common examples of a sequence and series would be Arithmetic Progression.
Eg: If a1,a2,a3, a4……. etc is considered to be a sequence, then the sum of terms in the sequence a1+a2+a3+ a4……. are considered to be a series.
Types of Sequence and Series:
Arithmetic Sequences
A sequence in which every term is created by adding or subtracting a definite number to the preceding number is an arithmetic sequence.
Geometric Sequences
A sequence in which every term is obtained by multiplying or dividing a definite number with the preceding number is known as a geometric sequence.
Harmonic Sequences
A series of numbers is said to be in harmonic sequence if the reciprocals of all the elements of the sequence form an arithmetic sequence.
Fibonacci Numbers
Fibonacci numbers form an interesting sequence of numbers in which each element is obtained by adding two preceding elements and the sequence starts with 0 and 1. Sequence is defined as, F0 = 0 and F1 = 1 and Fn = Fn-1 + Fn-2