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?
A. 10.5
B. 14.5
C. 18
D. 21.25
E. 39.5
Answer (3)
The sum of the first 4 terms of the arithmetic sequence where the 6th term is 8 and the 10th term is 13 is 14.5. ;
a 6 = 8 ; a 10 = 13 a 10 − a 6 = 4 r 4 r = 13 − 8 4 r = 5 / : 4 r = 1.25 a 1 = a 6 − 5 r a 1 = 8 − 5 ⋅ 1.25 = 8 − 6.25 = 1.75 S 4 = 2 2 a 1 + ( 4 − 1 ) r ⋅ 4 = ( 2 a 1 + 3 r ) ⋅ 2 = 4 a 1 + 6 r S 4 = 4 ⋅ 1.75 + 6 ⋅ 1.25 = 7 + 7.5 = 14.5
The sum of the first four terms of the arithmetic sequence is 14.5. This is calculated by finding the first term and common difference using the given terms of the sequence. The answer choice is B, 14.5.
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