If a sequence is as given below :
`1,1,2,3,5,8,13,21,34,….`
The unit digit of the sum of the 88th and 89th term of the same sequence will be :

Options

A. 5
B. 2
C. 0
D. none of these

Answer

To solve the problem, we need to find the 88th and 89th terms of the Fibonacci sequence and then calculate the unit digit of their sum.

### Step-by-Step Solution:

1. **Identify the Fibonacci Sequence**: The Fibonacci sequence starts with 1, 1, and each subsequent term is the sum of the two preceding terms. The sequence is:
- 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, 165580141, 267914296, 433494437, 701408733, 1134903170, 1836311903, 2971215073, 4807526976, 7778742049, 12586269025, 20365011074, 32951280099, 53316291173, 86267571272, 139583862445, 225851433717, 365435296162, 591286729879, 956722026041, 1548008755920, 2504730781961, 4052739537881, 6557470319842, 10610209857723, 17167680177565, 27777890035288, 44945570212853, 72723460248141, 117669030460994, 190392490709135, 308061521170129, 498454011879264, 806515533049393, 1304969544928657, 2111485077978050, 3416454622906707, 5527939700884757, 8944394323791464, 14472334024676221, 23416728348467685, 37889062373143906, 61305790721611591, 99294853094755497, 160500643816367588, 259695496911122585, 420196140727490173, 679891637638612758, 1100087778651109311, 1779979416289722069, 2880067194930831380, 4660046616220563449, 7540113801151394829, 12200160473791928278, 19740274274943323007, 31940434648735251285, 51680708854878574292, 83621143493513825577, 135301852344706999369, 218922995834555824946.

2. **Find the 88th and 89th Terms**:
- The 88th term (F(88)) can be calculated as F(86) + F(87).
- The 89th term (F(89)) can be calculated as F(87) + F(88).

3. **Calculate the Terms**:
- From the sequence, we can find:
- F(86) = 1100087778651109311
- F(87) = 1779979416289722069
- Therefore,
- F(88) = F(86) + F(87) = 1100087778651109311 + 1779979416289722069 = 2880067194930831380
- F(89) = F(87) + F(88) = 1779979416289722069 + 2880067194930831380 = 4660046616220563449

4. **Sum the Terms**:
- Now, we sum the 88th and 89th terms:
- Sum = F(88) + F(89) = 2880067194930831380 + 4660046616220563449 = 7540113801151394829

5. **Find the Unit Digit**:
- The unit digit of 7540113801151394829 is 9.

### Final Answer:
The unit digit of the sum of the 88th and 89th terms of the sequence is **9**.