what is the sum of the first sixteen terms of the arithmetic sequence 1,5,9,13...?
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what is the sum of the first sixteen terms of the arithmetic sequence 1,5,9,13...?
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Answer:
Given:
To find :
[tex]\sf{\underline{Solution:-}}[/tex]
Use the formula of finding sum to n terms in an AP.
★Formula to be used :
[tex]\boxed{S_n = \dfrac{n}{2} [2a + (n-1)d]}[/tex]
➣Puttng all the values :
➫[tex]S_{16} = \dfrac{16}{2} [2(1) + (16 - 1)4][/tex]
➫[tex]S_{16} = 8 [2 + 15(4)][/tex]
➫[tex]S_{16} = 8 [2 + 60][/tex]
➫[tex]S_{16} = 8 (62)[/tex]
➫[tex]S_{16} = 496[/tex]
•°•Sum of first 16 terms ia 496
SOLUTION
TO DETERMINE
The sum of the first sixteen terms of the arithmetic sequence 1 , 5 , 9 , 13 . . . .
EVALUATION
Here the given arithmetic sequence is
1 , 5 , 9 , 13 . . . .
First term = a = 1
Common Difference = d = 5 - 1 = 4
Number of terms = 16
Hence the required sum
[tex]\displaystyle \sf{ = \frac{n}{2} \bigg[ 2a + (n - 1)d\bigg] }[/tex]
[tex]\displaystyle \sf{ = \frac{16}{2} \bigg[ (2 \times 1) + 4(16 - 1)\bigg] }[/tex]
[tex]\displaystyle \sf{ = 8 \times \bigg[ 2 +60 \bigg] }[/tex]
[tex]\displaystyle \sf{ = 8 \times 62 }[/tex]
[tex]\displaystyle \sf{ = 496 }[/tex]
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