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Stels [109]
3 years ago
11

Find d for the sequence for which a1 = 100 and a12 = 34.

Mathematics
2 answers:
Crank3 years ago
6 0

Solution:

a_{1}=100, a_{12}=34

a_{12}=a_{1}+ 11 d \\\\ 34= 100+11 d\\\\ 34-100=11 d \\\\ -66=11 d \\\\ d=\frac{-66}{11}\\\\ d=-6

Option (A) -6 ,is correct common difference.

Marat540 [252]3 years ago
6 0

Answer:

Option a is correct.

d = -6

Step-by-step explanation:

An arithmetic sequence defined as the sequence of the number such that the Common difference of any two successive numbers of the sequence is constant.

The formula for nth term in the arithmetic sequence is,

a_n = a_1+(n-1)d               ......[1]

where

a_1 is the first term.

d is the common difference.

n is the number of terms.

Given that:  a_1 = 100 and a_{12} =34

Substitute n =12  and  a_1 = 100  in [1] we get

a_{12} = 100 +(12-1)d

a_{12} = 100 +11d

Substitute the value of  a_{12} =34 to solve for d;'

34 = 100+11d

Subtract 100 from both sides we get;

-66 = 11d

Divide both sides by 11 we get;

d = -6

Therefore, the common difference(d) for the given sequence is, -6

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