The arithmetic sequence has a 2nd term of -2 and a 7th term of 18 has the following answers.
What is arithmetic progression?
An progression or arithmetic sequence may be a sequence of numbers specified the difference between the consecutive terms is constant.
Main body:
General formula for arithmetic sequence
a + (n-1)d = aₙ
arithmetic sequence has a 2nd term of -2 , which means
a+d = -2
a = -(d+2) ---------(1)
7th term of 18 , which means
a+ 6d = 18
substituting value from equation 1,
-(d+2) +6d = 18
-d -2 +6d = 18
5d = 20
d = 5
using d= 5 in equation 1,
a = -(5+2)
a =-7
A) 10th term
=a +9d
= -7+9*5
= 38
B) recursive formula for the sequence = aₙ+1=aₙ+d .
Hence for the given sequence , it is
a₃ = a₂ +d
a₃ = -2+5
a₃ = 3
C) sum of first 10 terms
Sₙ = n/2{2a+ (n-1)d}
S₁₀ = 5 {2*-7 + 9*5}
S₁₀ = 5[ -14 +45]
S₁₀ = 5*31
= 105
Hence the sum of the first 10 terms is 105.\
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