For each of the following sequences find a functionansuch thatthe sequence is a1, a2, a3, . . ..
You're looking for a closed form - in particular, your answermay NOT be a recurrence (it may not involveany otherai). Also,while in general it is acceptable to use a "by cases"/piecewisedefinition, for this task you must instead present a SINGLEfunction that works for all cases.(Hint: you may find it helpful tofirst look at the sequence of differences of consecutiveterms.)
1) 7,1/11, 15,1/19, 23,1/27, 31,. . .
2) 1, 2, 2, 3, 3, 3, 4, 4, 4, 4,. . .where each i?N is repeatedi times. (Hint: one or more of the following may beuseful: floor function, Gauss sum, quadratic formula)
