sequence and series question (1 Viewer)

[bos1234]

Find the sum of the series
1,4,7,..., 1000

please show working

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Factorise

5(4^n - 1) - 5[4^(n-1) - 1]

 

[ianc]

okay with the first question it looks like an arithmetic series, so its just a matter of using simple 2unit formulas.

Find which term 1000 is in the series, using

T_n = a + r(n-1) {where a=1, r=3, T_n=1000}

Then use that value of n in this formula:

S_n = (n/2) [2a + r (n - 1)]




for the factorisation:

5(4ⁿ - 1) - 5[4^n-1 - 1]

= 5(4ⁿ) - 5 - 5(4^n-1) + 5
= 5(4ⁿ - 4^n-1)
= 5(4ⁿ)(1-4^-1)
= (15/4)(4ⁿ)