Summation of 3n + 2 from n = 1 to n = 14 = (3(1) + 2) + (3(2) + 2) + (3(3) + 2) + . . . + (3(14) + 2) = 5 + 8 + 11 + ... + 44 ia an arithmetic progression with first term (a) = 5, common difference (d) = 3 and last term (l) = 44 and n = 14
Sn = n/2(a + l) = 14/2(5 + 44) = 7(49) = 343
Therefore, the required summation is 343.
Steps to solve:
3(x - 1) = 5x + 3 - 2x
~Distribute left side
3x - 3 = 5x + 3 - 2x
~Combine like terms
3x - 3 = 3x - 3
~Subtract 3x to both sides
-3 = -3
~Add 3 to both sides
0 = 0
All real numbers are solutions.
Best of Luck!
Answer:
length = 20cm
breadth = 8cm
Step-by-step explanation:
solution;
length(l) = x + 12
breadth(b) = x
perimeter (p) = 56 cm
we know that,
perimeter(p) = 2(l + b)
or, 56 = 2(x + 12 + x)
or, 56 = 2(2x + 12)
or, 56 = 4x +24
or, 56 - 24 = 4x
or, 32 = 4x
or, 32 / 4 = x
x = 8
now
putting the value of x in length and breadth
length = x+ 12
=8 + 12
=20cm
breadth = 8cm
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Step-by-step explanation:
