Answered

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

Verified Answer :

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

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