Home
Class 12
MATHS
The number of terms common to the two A....

The number of terms common to the two A.P 's 3,7,11,……, 407 and 2,9,16,….709 is ____________

A

14

B

21

C

28

D

35

Text Solution

Verified by Experts

The correct Answer is:
A
Sequence `3,7,11,"…,"407` has commin difference =4 and sequence `2,9,16,"…..,"709` has common difference =7.
Hence, the sequence with common terms has common difference LCM of 4and 7 which is 28.
The first common term is 23.
Hence, the sequence is `23, 51,79,"....,"387` which has 14 terms.
Aliter By inspection, first common term to both the series is 23, second common term in 51, third common term is 79 and so on. These numbers form an AP`23,51,79,"..."`
Since, `T_(14)=23+13(28)=387lt407`
and `T_(15)=23+14(28)=415gt407`
Hence, number of common terms =14
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the number of terms in each of the following AP : 7,13,19,.....,205

The sum of …….terms of on A.P. 3, 7, 11, 15,….. Will becomes 406

Find the sum of indicated number of terms in each of the following Aps (i) 16, 11,6,….., 23 terms (ii) -0.5, -1.0, -1.5 ,………,10 terms (iii) -1,1/4,3/2 ,…..10 terms

If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term.

Check whether -150 is a term of the AP : 11 , 8 , 5, 2 .....

The 10th common term between the series 3+7+11+ . . . And 1+6+11+ ....... is

Check whether , -150 is a term fo the AP: 11,8,5,2,…..

How many terms of the A.P. 18, 16, 14, 12,…. are needed to give the sum 78?

The ratio of sums of n terms of two A.P'. is (7n + 1) : (4n + 27). Find the ratio of their 11th terms.

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