NCERT Solutions Class 9 Maths Chapter 8 Predicting What Comes Next: Exploring Sequences and Progressions on Padhaiwise

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 8 Predicting What Comes Next Exercise Set 8.1

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 8 — Exercise Set 8.1#

An explicit rule gives the $n^{th}$ term directly from $n$ (for example $t_n = 5n - 3$). A recursive rule gives each term from the terms before it (for example $t_{n+1} = t_n + 3$), together with the starting term(s).

To check whether a number is a term: set $t_n$ equal to it and solve for $n$. It is a term only if $n$ comes out as a natural number.

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 8 Predicting What Comes Next Exercise Set 8.2

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 8 — Exercise Set 8.2#

For an arithmetic progression (AP) with first term $a$ and common difference $d$:
$$t_n = a + (n - 1)d$$

$$\text{Recursive rule: } t_1 = a, \quad t_{n+1} = t_n + d$$

$$S_n = \dfrac{n}{2}\bigl(2a + (n - 1)d\bigr) = \dfrac{n}{2}(\text{first term} + \text{last term})$$

1. Find the 10th and 26th terms of the AP: 3, 8, 13, 18, …. #

Solution

Here $a = 3$ and $d = 8 - 3 = 5$.

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 8 Predicting What Comes Next Exercise Set 8.3

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 8 — Exercise Set 8.3#

For a geometric progression (GP) with first term $a$ and common ratio $r$:
$$t_n = a\,r^{\,n-1}$$

$$\text{Recursive rule: } t_1 = a, \quad t_{n+1} = r \times t_n$$

1. Find the 12th term of a GP with common ratio 2, whose 8th term is 192. #

Solution

From the 8th term to the 12th term we multiply by $r$ four times:

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 8 Predicting What Comes Next End-of-Chapter Exercises

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 8 — End-of-Chapter Exercises#

AP: $t_n = a + (n - 1)d$, $\quad S_n = \dfrac{n}{2}\bigl(2a + (n - 1)d\bigr)$

GP: $t_n = a\,r^{\,n-1}$

Sum of the first $n$ natural numbers: $\dfrac{n(n + 1)}{2}$

1. Find the 31st term of an AP whose 11th term is 38 and 16th term is 73. #

Solution

The 11th term is 38, so: