kalakadu.com: 24

Solution :

Since the given sequence is an arithmetic progression,

t2 - t1 = 10 - x ---(1)

t3 - t2 = y - 10 ---(2)

t4 - t3 = 24 - y ---(3)

t5 - t4 = z - 24 ---(4)

(1) = (2)

10 - x = y - 10

x + y = 20

(2) = (3)

y - 10 = 24 - y

y + y = 24 + 10

2y = 34

y = 17

By applying the value of y in x + y = 20

x + 17 = 20

x = 3

(3) = (4)

24 - y = z - 24

y + z = 24 + 24

y + z = 48

17 + z = 48

z = 31

Hence the values of x, y and z are 3, 17, 31 respectively.

Find the next three terms of the following sequence.

(i) 8, 24, 72, …

Solution :

To find the next three, first we have to find out the pattern followed in sequence.

Pattern :

Multiplying the first term by 3, we get the second term.Multiplying the second term by 3, we get the third term.

4th term = 3 (72) = 216

5th term = 216 (3) = 648

6th term = 648(3) = 1944

Hence the next three terms are 216, 648, 1944.