Get expert insights and community-driven knowledge on IDNLearn.com. Our experts provide accurate and detailed responses to help you navigate any topic or issue with confidence.
Sagot :
To find the 15th term of an Arithmetic Progression (AP) where the first term is given as [tex]\( a = 42 \)[/tex] and the 10th term ([tex]\( T_{10} \)[/tex]) is 210, we can follow these steps:
1. Determine the common difference [tex]\( d \)[/tex]:
The formula for the nth term [tex]\( T_n \)[/tex] of an AP is given by:
[tex]\[ T_n = a + (n - 1) \cdot d \][/tex]
For the 10th term:
[tex]\[ T_{10} = a + 9d \][/tex]
Substituting the given values:
[tex]\[ 210 = 42 + 9d \][/tex]
Solving for [tex]\( d \)[/tex]:
[tex]\[ 210 - 42 = 9d \][/tex]
[tex]\[ 168 = 9d \][/tex]
[tex]\[ d = \frac{168}{9} \][/tex]
Thus, the common difference [tex]\( d \)[/tex] is approximately [tex]\( 18.666666666666668 \)[/tex].
2. Calculate the 15th term ([tex]\( T_{15} \)[/tex]):
Using the formula [tex]\( T_n = a + (n - 1) \cdot d \)[/tex] again:
[tex]\[ T_{15} = a + 14d \][/tex]
Substituting the values for [tex]\( a \)[/tex] and [tex]\( d \)[/tex]:
[tex]\[ T_{15} = 42 + 14 \cdot 18.666666666666668 \][/tex]
Evaluating the expression:
[tex]\[ T_{15} = 42 + 261.33333333333337 \][/tex]
[tex]\[ T_{15} = 303.33333333333337 \][/tex]
Therefore, the 15th term of the Arithmetic Progression is [tex]\( 303.33333333333337 \)[/tex].
1. Determine the common difference [tex]\( d \)[/tex]:
The formula for the nth term [tex]\( T_n \)[/tex] of an AP is given by:
[tex]\[ T_n = a + (n - 1) \cdot d \][/tex]
For the 10th term:
[tex]\[ T_{10} = a + 9d \][/tex]
Substituting the given values:
[tex]\[ 210 = 42 + 9d \][/tex]
Solving for [tex]\( d \)[/tex]:
[tex]\[ 210 - 42 = 9d \][/tex]
[tex]\[ 168 = 9d \][/tex]
[tex]\[ d = \frac{168}{9} \][/tex]
Thus, the common difference [tex]\( d \)[/tex] is approximately [tex]\( 18.666666666666668 \)[/tex].
2. Calculate the 15th term ([tex]\( T_{15} \)[/tex]):
Using the formula [tex]\( T_n = a + (n - 1) \cdot d \)[/tex] again:
[tex]\[ T_{15} = a + 14d \][/tex]
Substituting the values for [tex]\( a \)[/tex] and [tex]\( d \)[/tex]:
[tex]\[ T_{15} = 42 + 14 \cdot 18.666666666666668 \][/tex]
Evaluating the expression:
[tex]\[ T_{15} = 42 + 261.33333333333337 \][/tex]
[tex]\[ T_{15} = 303.33333333333337 \][/tex]
Therefore, the 15th term of the Arithmetic Progression is [tex]\( 303.33333333333337 \)[/tex].
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com is your reliable source for accurate answers. Thank you for visiting, and we hope to assist you again.