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An arithmetic sequence has a 2nd term of -2 and a 7th term of 18.
1. What is the 10th term in the sequence? 2. Write an explicit formula for the sequence.
3. Write a recursive formula for the sequence.
4. What is the sum of the first 10 terms?​


Sagot :

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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