The sum of the third and the seventh terms of an A . P . is 6 and their product is 8 . Find the sum of first sixteen terms of the A . P .

Given that, a 3 + a 7 = 6 and a 3 a 7 = 8 . n t h term of an AP is given by a n = a 1 + ( n - 1 ) d , where a 1 is first term and d is common difference of AP . So, a 3 + a 7 = a 1 + 2 d + a 1 + 6 d ⇒ 2 a 1 + 8 d = 6 ⇒ a 1 + 4 d = 3 ...(i) Again, a 3 a 7 = a 1 + 2 d a 1 + 6 d ⇒ ( 3 - 4 d + 2 d ) ( 3 - 4 d + 6 d ) = 8 [ from (i) ] ⇒ ( 3 - 2 d ) ( 3 + 2 d ) = 8 ⇒ 9 - 4 d 2 = 8 ⇒ 1 = 4 d 2 ⇒ d 2 = 1 4 ⇒ d = ± 1 2 From (i), a 1 + 4 d = 3 ⇒ a 1 = 3 - 4 d ⇒ a 1 = 3 - 4 1 2 , when d = 1 2 ⇒ a 1 = 1 , when d = 1 2 ⇒ a 1 = 3 - 4 - 1 2 , when d = - 1 2 ⇒ a 1 = 5 , when d = 1 2 Sum of n terms of an AP is S n = n 2 2 a 1 + ( n - 1 ) d . S 16 = 16 2 2 ( 1 ) + 15 1 2 , a = 1 and d = 1 2 ⇒ S 16 = 8 19 2 ⇒ S 16 = 76 S 16 = 16 2 2 ( 5 ) + 15 - 1 2 , a = 5 and d = - 1 2 ⇒ S 16 = 8 10 - 15 2 ⇒ S 16 = 8 5 2 ⇒ S 16 = 20 ∴ Sum of first 16 terms of given AP is 76 or 20 .

HARD

11th ICSE

IMPORTANT

Earn 100

Divide $32$ into four parts which are in $A . P .$ such that the product of extremes is to the product of means is $7 : 15$ .

Important Questions on Sequences and Series

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.3>Q 19

The sum of the third and the seventh terms of an

A . P .

6

and their product is

8

. Find the sum of first sixteen terms of the

A . P .

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.3>Q 19

The houses of a row are numbered from

1

49

. Show that there is a value of

n

such that the sum of the numbers of the houses preceding the house numbered

n

is equal to the sum of the numbers of the houses following it. Find this value of

n

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.3>Q 20

A man accepts a position with an initial salary of

₹ 5200

per month. It is understood that he will receive an automatic increase of

₹ 320

in the very next month and each month thereafter. Find his salary for the tenth month.

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.3>Q 20

A man accepts a position with an initial salary of

₹ 5200

per month. It is understood that he will receive an automatic increase of

₹ 320

in the very next month and each month thereafter. What is his total earnings during the first year?

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.3>Q 21

A person buys every year National Savings Certificates of value exceeding the last year's purchase by

₹ 5000

. After

10

years, he finds the total face value of certificates purchased by him is

₹ 275000

. Find the value of the certificates purchased by him in the first year. Why do you think saving is important for both individuals and the country?

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.3>Q 22

A spiral is made of successive semicircles, with centres alternately at $A$ and $B$ , starting with centre at $A$ of radii $0.5 cm, 1.0 cm$ $1.5 cm, \dots$ as shown in the adjoining figure. What is the total length of such a spiral made up of thirteen consecutive semicircles. Take $π = \frac{22}{7}$ .

Question Image

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.3>Q 22

A ladder (shown in the figure) has rungs $25 cm$ apart. The rungs decrease uniformly in length from $45 cm$ at the bottom to $25 cm$ at the top. If the top and the bottom
rungs are $2 \frac{1}{2} m$ apart, what is the length of the wood required for the rungs?

Question Image

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 1>Chapter 10 - Sequences and Series>EXERCISE 10.3>Q 23

A carpenter was hired to build

192

window frames. The first day he made five frames and each day, thereafter he made two more frames than he made the day before. How many number of days did it take him to finish the job?

Divide 32 into four parts which are in A.P. such that the product of extremes is to the product of means is 7:15.

Important Questions on Sequences and Series

Learn and Prepare for any exam you want !

Divide $32$ into four parts which are in $A . P .$ such that the product of extremes is to the product of means is $7 : 15$ .