Question

Help me with this asap​

Answer 1

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