Question

8. Find the next term in the series. 28, 44,-81,-45, -388, ?​

Answer 1

Answer:

If we carefully observe the series, it can be seen that,

The difference between first two terms = 16 - 8 = 8

The difference between second and third term = 28 - 16 = 12

The difference between third and fourth term = 44 - 28 = 16

Going by this,

The difference between fourth and fifth term would be, X - 44 = 20

X = 44 + 20 = 64

Thus , the next term in the series would be 64.

Method 2:

Learning: The given series is not complete. It is missing the first element of the series i,.e, 2. So the correct series is,

2, 8, 16, 28, 44, ….

The generalized formula for the series is,

For n>1, a(n) = 2*(n^2 - n + 2)

n^2 means n raised to the power of 2 or in simple words, it is the square of n.

Applying the formula to find terms,

For (n = 2) = 2*(2^2 - 2 + 2) = 2*(4 - 2 + 2) = 8

For (n = 3) = 2*(3^2 - 3 + 2) = 2*(9 - 3 + 2) = 16

For (n = 4) = 2*(4^2 - 4 + 2) = 2*(16 - 4 + 2) = 28

For (n = 5) = 2*(5^2 - 5 + 2) = 2*(25 - 5 + 2) = 44

For (n = 6) = 2*(6^2 - 6 + 2) = 2*(36 - 6 +2) = 64

For (n = 7) = 2*(7^2 - 7 + 2) = 2*(49 - 7 + 2) = 88

and so on