Ryan was building matchstick square sequences. He used 4 matchsticksfornthe first, followed by, 7,10,13 and 67 matches to form the last square. How many matchsticks did he use for the entire project?
Answers
Answer:
total 781 matchsticks
Step-by-step explanation:
sequence of matchstics: 4,7,10,13_,_,_,67
common difference (d) = 3
first term (a) = 4
last term (L)= 67
for no. of terms (n)=> L = a+(n-1)d
=> 67 = 4+(n-1)3
=> 67-4 = (n-1)3
=> 63/3 = n-1
=> 63/3 +1 = n
=> n = 22
It forms an arithematic progression(A.P)
Using sum of A.P (s)=> n/2 [2a+ (n-1)d]
=> s = 22/2 [2x4 +(22-1)3]
=> s = 11 (8 +63)
=> s = 11x71
=> s = 781
he used total 781 matchsticks
Mark branliest if it help you
Given : He used 4 matchsticks for the first, followed by, 7,10,13 and 67 matches to form the last square.
To Find : How many matchsticks did he use for the entire project
Solution:
Arithmetic sequence : Sequence of terms in which difference between one term and the next is a constant.
This is also called Arithmetic Progression AP
Arithmetic sequence can be represented in the form :
a, a + d , a + 2d , …………………………, a + (n-1)d
a = First term
d = common difference = aₙ-aₙ₋₁
nth term = aₙ = a + (n-1)d
Sₙ = (n/2)(2a + (n - 1)d)
Sum of Arithmetic sequence (AP) is called Arithmetic series
a = 4
d = 7 - 4 = 10 - 7 = 3
last = 67
67 = 4 + (n - 1) 3
=> 63 = (n - 1)3
=> 21 = n - 1
=> n = 22
Sum of all = (n/2) ( first + last)
= (22/2) (4 + 67)
= 11 * 71
= 781
Total Matchsticks used = 781
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