Answer :

To Find: First four terms of given series.


(i) Given: nth term of series is (5n + 2)


Put n=1, 2, 3, 4 in nth term, we get first (a1), Second (a2), Third (a3) & Fourth (a4) term


a1 = (51 + 2) = 7


a2 = (52 + 2) = 12


a3 = (53 + 2) = 17


a4 = (54 + 2) = 22


First four terms of given series is 7, 12,17,22


ALTER: When you find or you have first term (a or a1) and second term (a2) then find the difference (a2 - a1)


Now add this difference in last term to get the next term


For example a1= 7 and a2= 12, so difference is 12 - 5 = 7


Now a3 = 12 + 5 = 17, a4 = 17 + 5 = 22


(This method is only for A.P)


NOTE: When you have nth term in the form of (an + b)


Then common difference of this series is equal to a.


This type of series is called A.P (Arithmetic Progression)


(Where a, b are constant, and n is number of terms)


(ii) Given: nth term of series is


Put n=1, 2, 3, 4 in nth term, we get first (a1), Second (a2), Third (a3) & Fourth (a4) term.


a1 = =


a2 = =


a3 = =


a4 = =


First four terms of given series are , , ,


(iii) Given: nth term of series is (–1)n–1 × 2n + 1


Put n=1, 2, 3, 4 in nth term, we get first (a1), Second (a2), Third (a3) & Fourth (a4) term.


a1 = (–1)1–1 × 21 + 1 = (–1)0 × 22 = 14 = 4


a2 = (–1)2–1 × 22 + 1 = (–1)1 × 23 = (–1)8 = (–8)


a3 = (–1)3–1 × 23 + 1 = (–1)2 × 24 = 116 = 16


a4 = (–1)4–1 × 24 + 1 = (–1)3 × 25 = (–1)32 = (–32)


First four terms of given series are 4, –8 , 16 ,–32


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