What is the sum of the first 4 terms of the arithmetic sequence in which the 6th term is 8 and the 10th term is 13?

1 Answer
May 5, 2016

Answer:

Sum of the first 4 terms is #14.50#

Explanation:

In an arithmetic sequence, whose first term is #a# and difference between a term and its preceding term is #d#,

the #n^(th)# term is #a+(n-1)d# and sum of first #n# terms is #n/2(2a+(n-1)d)#

Hence #6^(th)# term will be #a+5d=8# and #10^(th)# term will be #a+9d=13#

Subtracting first from second, #4d=5# or #d=1.25#

and #a=8-5*1.25=8-6.25=1.75#

Hence sum of first four terms is

#4/2*(2*1.75+3*1.25)=2*(3.5+3.75)=2*7.25=14.50#