Question

how many term of sequence 9,13,17 added gives the sum 624

Answer 1

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Here is the solution:

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Sequence = 9, 13, 17

Find a1:

a1 = first term = 9

Find d:

d = 13 - 9

d = 4

Form the AP:

General AP series : an = a1 + ( n - 1 ) d

an = 9 + ( n - 1)4

an = 9 + 4n - 4

an = 5 + 4n

Find n when sn = 624

sn = n/2 ( a1 + an)

624 = n/2 ( 9 + 5 + 4n)

1248 = n(14 + 4n)

1248 =14n+ 4n²

4n² + 14n - 1248 = 0

2n² + 7n - 624 = 0

(n - 16) (2n + 39) = 0

n = 16 or n = - 39/2 (rejected, since n cannot be negative)

Answer: There are 16 terms