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Find the value of U32 in the sequence Un = 7.6, Un = Un-1 + 3.1 where n ≥ 1.

A. 78.9
B. 99.2
C. 106.8
D. 246.3

1 Answer

3 votes

Final answer:

To find U32 in the given sequence, we can apply the recursive formula Un = Un-1 + 3.1 or add 3.1 to U1 repeatedly. The value of U32 is 103.7.

Step-by-step explanation:

To find the value of U32 in the given sequence, we can use the recursive formula provided: Un = Un-1 + 3.1.

Starting with U1 = 7.6, we can use the formula to find the subsequent terms:
U2 = U1 + 3.1 = 7.6 + 3.1 = 10.7
U3 = U2 + 3.1 = 10.7 + 3.1 = 13.8
...

Continuing this pattern, we can find U32 by applying the formula 31 times:
U32 = U31 + 3.1 = (U30 + 3.1) + 3.1 = ((U29 + 3.1) + 3.1) + 3.1 = ...

Alternatively, we can notice that each term in the sequence is 3.1 greater than the previous term. So, U32 can also be found by adding 3.1 to U1 repeatedly 31 times:
U32 = U1 + (31 x 3.1) = 7.6 + (31 x 3.1) = 7.6 + 96.1 = 103.7

Therefore, the value of U32 in the sequence is 103.7.

User Shadrack
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