# Geometric Progression

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• Q1

Sum to n terms of the series:
7 + 77 + 777 + ...

Marks:2

• Q2

Find the sum of the following series:
243 + 324 + 432 +....... to n terms.

Marks:3

• Q3

Find the GP whose 4th term is 54 and the 7th term is 1458.

Marks:1

We have,

t4 = ar3 = 54 ...(1)

t7 = ar6 = 1458 ...(2)

Dividing (2) from (1), we get

r3 = 1458/54 = 27

or r = 3

Therefore, from (1), we get
27a = 54

or a = 2.

Hence, the GP is 2, 6, 18, 54,...

• Q4

Find the nth term of the sequence 2, 6, 18, ...

Marks:1

Here a = 2, r = 6/2 = 3.

Therefore, nth term Tn = arn-1 = 2 x 3n-1.

• Q5

The first three terms of a geometric sequence are 48, 24 and 12. what are the common ratio and fourth term of this sequence?

Marks:1

To find the common ratio, divide any term by its predecessor.

24/48 = 1/2 or 12/24 = 1/2

Therefore, the common ratio is 1/2

Now we have to find the fourth term for that we need to multiply the third term by the common ratio 12 x 1/2 = 6.

Hence, the fourth term is 6.