Find the sum up to #n# terms of the series #2.3,4.5,6.7,8.9,..................#?

1 Answer
Nov 3, 2017

Sum up to #n# terms in the given series is #1.1n^2+1.2n#

Explanation:

As we have #8.9-6.7=6.7-4.5=4.5-2.3=2.2#

this is an arithmetic series with first term #a_1=2.3# and common difference #d# as #2.2#.

Sum #S_n# up tp #n# terms of an arithmetic series whose first term is #a_1# and common difference #d# is

#S_n=n/2(2a+(n-1)d)#

Hence sum up to #n# terms in the given series is

#S_n=n/2(2xx2.3+(n-1)2.2)#

= #n/2(4.6+2.2n-2.2)#

= #n/2(2.2n+2.4)#

= #n(1.1n+1.2)#

= #1.1n^2+1.2n#