The sum of the second, eighth and eleventh term of the arithmetic progression is 69.
| September 12, 2021 | education
The sum of the second, eighth and eleventh term of the arithmetic progression is 69. Find the seventh term of this progression.
We use the formula for the nth term of the arithmetic progression.
an = a1 + d * (n – 1).
a2 = a1 + d.
a8 = a1 + 7 * d.
a11 = a1 + 10 * d.
a1 + d + a1 + 7 * d + a1 + 10 * d = 69.
3 * a1 + 18 * d = 69.
Divide both sides of the equality by 3.
a1 + 6 * d = 23.
a1 + 6 * d = a1 + d * (7 – 1), which is the seventh member of the progression.
a7 = 23.
Answer: The seventh member of the progression is 23.
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