How do I find the sum of the arithmetic sequence 3, 5, 7, 9, ..., 21?

2 Answers

#120#

Explanation:

Given arithmetic sequence

#3, 5, 7, 9, ........., 21#

The first term #a=3# & a common difference #d=5-3=7-5=\cdots=2#

If there are #n# number of terms in the above A.P. then last term #l=21# will be the nth term given as

#l=a+(n-1)d#

#21=3+(n-1)2#

#n=10#

hence the sum of given arithmetic progression (#A.P.#) up to #10# terms is given general formula

#S_n=\frac{n}{2}(a+l)#

#S_10=\frac{10}{2}(3+21)#

#=120#

Jul 11, 2018

#S_(10)=120#

Explanation:

#"the sum to n terms of an arithmetic sequence is"#

#•color(white)(x)S_n=n/2[2a+(n-1)d]#

#"where a is the first term and d the common difference"#

#"here "a=3,d=7-5=5-3=2,n=10#

#S_(10)=5[(2xx3)+(2xx9)]#

#color(white)(xx)=5(6+18)=120#