Consider the arithmetic sequence1,4,7........ a)Find the common difference b)Write the algebraic expression of this sequence c)Find the 50th term of the above sequence d)Is 2020 is a term? e)Find the sum of the first 100 terms of this sequence *
Answers
Answer:
Step-by-step explanation:
the sequence is 1,4,7,....
a) common difference, d = a₂ - a₁
= 4-1 = 3
b) first term, f = 1
Xₙ = dn+(f-d)
= 3n+(1-3)
= 3n+-2
= 3n-2
c) to find 50th term, put n=50 in Xₙ
X₅₀ = 3×50 - 2
= 150 -2
= 148
d) let Xₙ be 2020,
3n-2 = 2020
3n = 2022
n = 2022/3
= 674
2020 is a term, 674th term is 2020
e) X₁₀₀ = 3×100 -2
= 300-2
= 298
sum = n/2 [X₁+Xₙ]
= 100/2 [X₁+X₁₀₀]
= 50 [1+298]
= 50×299
= 14950
sum of first 100 terms is 14950