The 6th and 11th terms of an arithmetic sequence are 38 and 73.find the first term and write the algebric expression of the sequence
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Step-by-step explanation:
a6 = 38.
a + 5d = 38
a = 38 - 5d.......equation 1
a11 = 73.
a + 10d = 73
38 - 5d + 10d = 73........from equation 1
38 + 5d = 73
5d = 73 - 38
5d = 35
d = 35/5
d = 7
Put d = 7 in equation 1
a = 38 - 5 (7)
a = 38 - 35
a = 3
Therefore ; the first term (a) = 3
a2 = a+d a3 = a +2d. a4 = a + 3d
= 3+7 = 3 + 2(7). = 3 + 3(7)
= 10. = 3 + 14. = 3 + 21
= 17. = 24
Therefore :the A.P. is 3, 10, 17, 24
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