Question

Here is the sequence; 5, 11, 21, 35, ...
The next three terms of this sequence are 65 and 85 true or false?

Answer 1

Step-by-step explanation:

What is the next term of 5, 11, 21, 35, 53?

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Let nth term of 5, 11, 21, 35, 53… be An

d1=a2−a1=6

d2=a3−a2=10

d3=a4−a3=14

We can see that the difference between consecutive terms is in with first term being 6 and the common difference being 4.

In order to find An we need to add the first term, 5 to the sum of the common difference. And, since the first term of the progression doesn’t require the addition of the difference, the difference is added from the second term onwards.

Finding sum of difference:

Sum of AP = Sn=n2(2a+(n−1)d)

On replacing the values of a and d with 6 and 4 respectively:

Sn=n2(12+4n−4)

Sn=n2(8+4n)

Sn=n(4+2n)

Sn=4n+2n2

Finding An

Thus, An would equal first term + sum of (n−1) differences

An=5+4(n−1)+2(n−1)2

An=5+4(n−1)+2(n−1)(n−1)

An=5+2(n−1)(n−1+2)

An=5+2(n−1)(n+1)

An=5+2(n2−1)

An=5+2n2−2

An=2n2+3

Thus the next term (6th) would be 75.

hope this helps you