Question

Evaluate each series to the given term. 2+4+6+8+ . . . . . . ; 10 th term

Answer 1

Finding the value of any term in a given sequence is known as an arithmetic sequence if each term in the sequence is equidistant from the terms before and after. To find any term in a sequence, we first have to find the pattern of the sequence. Then we can multiply the distance between any two terms by one less than the number of terms we are looking for. Adding this to the first term gives you the term you want.

Here the first term a=2,

Common difference d=4-2=2

We know that,

f(n)=a+(n-1) d

f (10) =2+(10-1) (2)

=2+(18)

=20

We know that,

Sn=n2[2a+(n-1) d]

∴S10=102⋅ [2(2) +(10-1) (2)]

=5⋅ [4+(18)]

=5⋅ [22]

=110

Hence, the 10th term of the given series is 20, and the sum of the first 10th term is 110.

More problems related to a similar concept are solved in the link below.

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