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Suatu barisan aritmatika dengan

U_(4)+U_(8)+U_(11)+U_(17)=316.
Nilai
U_(10) adalah
(A) 80
(B) 79
(C) 78
(D) 77
(E) 76

$1$ . Suatu barisan aritmatika dengan $\newline$ $\mathrm{U}_{4}+\mathrm{U}_{8}+\mathrm{U}_{11}+\mathrm{U}_{17}=316 .$ $\newline$ Nilai $\mathrm{U}_{10}$ adalah $\newline$ (A) $80$ $\newline$ (B) $79$ $\newline$ (C) $78$ $\newline$ (D) $77$ $\newline$ (E) $76$

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Roots of rational numbers

Full solution

Q.

1

. Suatu barisan aritmatika dengan

\newline

\mathrm{U}_{4}+\mathrm{U}_{8}+\mathrm{U}_{11}+\mathrm{U}_{17}=316 .

\newline

Nilai

\mathrm{U}_{10}

adalah

\newline

(A)

80

\newline

(B)

79

\newline

(C)

78

\newline

(D)

77

\newline

(E)

76

Define Terms: Let's denote the first term of the sequence as $a$ and the common difference as $d$ . The $n$ th term of an arithmetic sequence is given by $U_n = a + (n-1)d$ .
Write Given Terms: We can write the given terms using the formula for the nth term: $U_4 = a + 3d$ $U_8 = a + 7d$ $U_{11} = a + 10d$ $U_{17} = a + 16d$
Add Given Terms: Now, let's add these up as per the given equation: $\newline$ $U_4 + U_8 + U_11 + U_17 = (a + 3d) + (a + 7d) + (a + 10d) + (a + 16d) = 316$
Simplify Equation: Simplify the equation: $4a + 36d = 316$
Introduce Another Equation: We need to find $U_{10}$ , which is $a + 9d$ . But we only have one equation and two unknowns. We need another equation to solve for $a$ and $d$ .
Apply Spacing Property: Notice that the terms are evenly spaced, so the sum of pairs equidistant from the ends should be equal. That means $U_4 + U_{17} = U_8 + U_{11}.$
Simplify Equation: Let's write that out: $\newline$ $(a + 3d) + (a + 16d) = (a + 7d) + (a + 10d)$
Subtract Terms: Simplify the equation: $2a + 19d = 2a + 17d$
Subtract Terms: Simplify the equation: $\newline$ $2a + 19d = 2a + 17d$ Subtract $2a$ from both sides: $\newline$ $19d = 17d$

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