Answer:
Sum = 795
Explanation:
an = a + (n - 1)*d
16th Term
a_16 = a + (16 - 1) * d
a_16 = a + 15 * d
53 = a + 15 d
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a_20 = a + 19*d
65 = a + 19d
53 = a + 15d Subtract
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12 = 4d Divide by 4
3 = d
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53 = a + 15d
53 = a + 15*3
53 = a + 45
a = 53 - 45
a = 8
The first odd term in the sequence is 8 + 3 = 11
The next term is 11 + 3 = 14
The third term is 17
So the difference is 17 - 11 = 6
The last term is
L = a + (n - 1)*6
L = 11 + (n - 1)*6
I think we have to guess at what the last term is. Let n = 10
L = 11 + 9*6 It's not large enough
Try 15
L = 11 + 14*6
L = 11 + 84
L = 95 That's correct. The last term in the sequence is 95
So
The sum is
Sum = (a + L)*n/2
n = 15
Sum = (11 + 95)*15/2
Sum = (106)*15/2
Sum = 53*15/2
Sum = 795