Given the string (an),n>=1 and the sum a1+a2+a3+...+an=(5n^2+6n), what are an and a1?

Expert Answers

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We are given that a1 + a2 + a3 + ... + an = (5n^2+6n).

Sn = a1 + a2 + a3 + ... + an = (5n^2+6n).

Sn+1 = a1 + a2 + a3 + ... + an + an+1 = (5(n+1)^2+6(n+1)).

Sn+1 - Sn

=> a1 + a2 + a3 + ... + an + an+1 - a1 + a2 + a3 + ... + an = (5(n+1)^2+6(n+1)) - (5n^2+6n)

=> an+1 = 5n^2 + 5 + 10n + 6n + 6 - 5n^2 - 6n

=> an+1 = 5 + 10n + 6

=> an+1 = 10n + 11

=> an = 10(n-1) + 11

=> an = 10n - 10 + 11

=> an = 10n + 1

a1 = 10n + 1 = 11

The required value of an = 10n + 1 and a1 = 11

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