Question 1187314
<br>
The first 16 terms are<br>
a, a+d, a+2d, ..., a+14d, a+14d<br>
Combining like terms, the sum of the first 16 terms is<br>
16a + (1+2+3+...+14+15)d = 16a+120d<br>
The first term is 12; the sum of the first 16 terms is 282:
16(12)+120d = 282
192+120d = 282
120d = 90
d = 3/4<br>
ANSWER a): the common difference is 3/4<br>
1st term: 12
5th term: 12+4(3/4) = 12+3 = 15<br>
The 1st and 5th terms of the arithmetic progression are the 1st and second terms of a geometric progression.<br>
common ratio: 15/12 = 5/4<br>
3rd term in the geometric progression: 15(5/4) = 75/4 = 12+27/4 = 12+9d, which is the 10th term of the arithmetic progression.<br>
The 3rd term of the geometric progression is the 10th term of the arithmetic progression.<br>
ANSWER b): common ratio 3/4; n=10<br>