The 4 th term of an arithmetic progression is 22 and 15 th term is 66 . Find the first term and the common difference. Hence, find the sum of the series to 8 terms.

Let the first term be a and the common difference be d Given, a 4 = 22 , a 15 = 66 We know, a 4 = a + 3 d = 22 . . . ( i ) and a 15 = a + 14 d = 66 . . . ( i i ) Subtracting ( i ) from ( i i ) , we get ⇒ ( a + 14 d ) - ( a + 3 d ) = 66 - 22 ⇒ 11 d = 44 ⇒ d = 44 11 = 4 Putting this value of d in ( i ) , ⇒ a + 3 × 4 = 22 ⇒ a = 22 - 12 = 10 Now, ∴ S 8 = 8 2 2 × 10 + ( 8 - 1 ) × 4 ⇒ S 8 = 4 × 20 + 7 × 4 ⇒ S 8 = 4 × 20 + 28 ⇒ S 8 = 4 × 48 = 192

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Arithmetic and Geometric Progression>ICSE-2019>Q 4

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10th ICSE

IMPORTANT

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In an Arithmetic progression (A.P.), the fourth and sixth terms are $8$ and $14$ respectively. Find the first term.

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Important Questions on Arithmetic and Geometric Progression

EASY

10th ICSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Arithmetic and Geometric Progression>ICSE-2019>Q 5

In an Arithmetic Progression (A.P.) the fourth and sixth terms are $8$ and $14$ respectively. Find the common difference.

EASY

10th ICSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Arithmetic and Geometric Progression>ICSE-2019>Q 6

In an Arithmetic Progression

(AP)

the fourth and sixth terms are

8

and

14

respectively. Find the sum of the first

20

terms.

MEDIUM

10th ICSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Arithmetic and Geometric Progression>ICSE-2019>Q 7

The first and last term of a Geometric Progression (GP) are

3

and

96

, respectively. If the common ratio is

2

, then find

n

in the number of terms of the

G P

.

EASY

10th ICSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Arithmetic and Geometric Progression>ICSE-2019>Q 8

The first and last term of a Geometric Progression (GP) are

3

and

96

, respectively. If the common ratio is

2

, then find sum of

n

terms.

MEDIUM

10th ICSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Arithmetic and Geometric Progression>ICSE-2019>Q 9

The sum of the first three terms of an Arithmetic Progression (A.P.) is $42$ and the product of the first and third term is $52$ . Find the first term and the common difference.

MEDIUM

10th ICSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Arithmetic and Geometric Progression>ICSE-2020>Q 10

The