Question

a. How many numbers are there in the 30th row of this number pyramid?

b. Which is the last number in the 30th row?

c. Which is the first number in the 30th row?

d. What is the sum of all terms in the first 30 rows?

Answer 1

a. Total numbers in each sequence can be written as

1, 3, 5, …. xn = 2_n – 1

Numbers in the 30th row = 2 x 30 – 1 = 59

b. Last number in the first row = 12 = 1

Last number in the second row = 22 = 4

Last number in the third row = 32 = 9

Last number in thew 30th row = 302 = 900

c. Number of terms in the 30th row = 59

Last number in the 30th row = 900

First number in the 30th row + 58d = Last term in the 30th row

First number in the 30th row + 58 x 1 = 900 First 

number in the 30th row = 900 – 58 = 842

d. The sum of all terms in the first 30 rows = \(\frac{900\times901}{2}\)

= 450 × 901 = 405540

Arithmetic Sequences Memory Map