Question

The sum of 13 terms of an arithmetics progression is 286 and the common difference is 3. Determine the first term of the series.

Answer 1

Answer:an=3n+1 with a=4 and d=3

Step-by-step explanation:

Sum of 13 terms is 286

d=3

13/2(2a+12d)=286

13/2(2a+36)=286

13(a+18)=286

a+18=22

a=4

So nth term is a+(n-1)d

=4+(n-1)3

=3n+1

Answer 2

The correct answer is 4.

Given: The sum of 13 terms of an arithmetic progression = 286.

Common difference = 3.

To Find: First term of series.

Solution:

Sum of series = $\frac{n}{2}(2a+(n-1)d)$

Where, n is number of terms, a is first term and d is common difference.

$\frac{13}{2}(2a+(13-1)3)=286$

$2a+12*3=44$

2a = 8

a = 4

Hence, the first term of series is 4.

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