Mathematics

# 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 ? F. 10.5 G. 14.5 H. 18 J. 21.25 K. 39.5

$a_6=8;\ a_{10}=13\\\\a_{10}-a_6=4r\\\\4r=13-8\\4r=5\ \ \ \ /:4\\r=1.25\\\\a_1=a_6-5r\\a_1=8-5\cdot1.25=8-6.25=1.75\\\\S_4=\frac{2a_1+(4-1)r}{2}\cdot4=(2a_1+3r)\cdot2=4a_1+6r\\\\S_4=4\cdot1.75+6\cdot1.25=7+7.5=14.5$