Answer:

a10= 2/55

Step-by-step explanation:

a1 =2/37

a15 = 2/65

harmonic sequence is reciprocal of terms form an arithmetic sequence

so were just going to make it in reciprocal

a1= 37       a15 = 65

since there's no common difference, we need to find it first

we use a1+nd  and an = a1 +(n-1)d to find the d

we knew that  15th term has the form  37+ 14d  

    were going to substitute the 14d  in (n-1)d  

sol.

an = a1 + (n-1)d  

a15 = 37 + 14d

65 +  37 + 14d        substitute the value

65-37 = 14d

28 = 14d

28/14 = 14d/14        

2 = d

then find the 10th term

an = a1 +(n-1)d

a10=37 +(10-1)2            substitute the value

     = 37 + (9)2

     = 37+18

     = 55

we just need to back it in reciprocal

so the answer is 2/55

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