Examples of Math Problems: The 4th and 15th term of an arithmetic progression are -30 and 10 respectively. find the arithmetic progression and it's 20th term.

Friday, January 17, 2014

The 4th and 15th term of an arithmetic progression are -30 and 10 respectively. find the arithmetic progression and it's 20th term.

We can use the typical equations for arithmetic sequences, with some "twists"
a%5B4%5D=-30

a%5B4%5D=-30

a%5B15%5D=10

Common difference works like slope, so...
d=%28a%5Bn%5D-a%5Bm%5D%29%2F%28n-m%29=%2810-%28-30%29%29%2F%2815-4%29=40%2F11

d=%28a%5Bn%5D-a%5Bm%5D%29%2F%28n-m%29=%2810-%28-30%29%29%2F%2815-4%29=40%2F11

Now we can find the first term...
a%5B1%5D=a%5Bn%5D-%28n-1%29d=-30-%284-1%29%2840%2F11%29=-450%2F11

a%5B1%5D=a%5Bn%5D-%28n-1%29d=-30-%284-1%29%2840%2F11%29=-450%2F11

so that

a%5Bn%5D=-450%2F11%2B%28n-1%29%2840%2F11%29

and so

a%5B20%5D=-450%2F11%2B%2820-1%29%2840%2F11%29=310%2F11

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