a[25]=1.7, d=0.6
In general,
a[n] = a[1] + d(n-1)
1.7 = a[25] = a[1] + 0.6(25 - 1)
a[1] = 1.7 - 0.6(24) = -12.7
a[n] = -12.7 + 0.6(n - 1)
Answer a[1]=-12.7
Filling in the boxes,
a[1]=-12.7, a[2]=-12.1, a[3]=-11.5, a[4]=-10.9, a[5]=-10.3, a[6]=-9.7
check that last one with the formula, a[6]=-12.7-.6(6-1) = -9.7, good
we're asked for a recursive formula, which is easier,
Answer: a[n] = a[n-1] + 0.6
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a[n] = a[1] + d(n-1)
a[23] = 21 = a[1] + 22d
a[43] = 61 = a[1] + 42d
Subtracting,
40 = 20d
d = 2
21 = a[1] + 22(2)
a[1] = 21 - 44 = -23
Answer: a[1] = -23, a[n] = a[n-1] + 2
Check: a[n]=-23 + 2(n-1) at n=43 gives a[43]=-23 +2(42) =61, good
