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 = (5 × 1 + 2) = 7
a2 = (5 × 2 + 2) = 12
a3 = (5 × 3 + 2) = 17
a4 = (5 × 4 + 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 (a × n + 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 (2n - 3)/4
Put n = 1, 2, 3, 4 in nth term, we get
first (a1), Second (a2), Third (a3) & Fourth (a4) term.
First four terms of given series are -1/4, 1/4, 3,4, 5/4
(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 = 1 × 4 = 4
a2 = (–1)2–1 × 22 + 1 = (–1)1 × 23 = (–1) × 8 = (–8)
a3 = (–1)3–1 × 23 + 1 = (–1)2 × 24 = 1 × 16 = 16
a4 = (–1)4–1 × 24 + 1 = (–1)3 × 25 = (–1) × 32 = (–32)
First four terms of given series are 4, –8 , 16 ,–32