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When we add odd numbers:

1 = 1

1 + 3 = 4

1 + 3 + 5 = 9

...

Notice that the sum of n terms is n²

* This is because an odd number is expressed as 2n-1, we would need to get the sum of all 2n-1 substituting the value from 1 to n. (This is summation)

So we would have 2(1+2+3+...+n) - n = 2[n(n+1)/2] - n = n(n+1) - n = n(n+1-1) = n²

So:

Sum of n terms = 961

Sum of n terms = 31² = n²

n = 31

There are 31 terms in the arithmetic sequence

1 = 1

1 + 3 = 4

1 + 3 + 5 = 9

...

Notice that the sum of n terms is n²

* This is because an odd number is expressed as 2n-1, we would need to get the sum of all 2n-1 substituting the value from 1 to n. (This is summation)

So we would have 2(1+2+3+...+n) - n = 2[n(n+1)/2] - n = n(n+1) - n = n(n+1-1) = n²

So:

Sum of n terms = 961

Sum of n terms = 31² = n²

n = 31

There are 31 terms in the arithmetic sequence