Question

3,7,11.....407
nd 2,9,16....709
find num of common terms

Answer 1

answer it fast

Answer 2

3,7,11.....407 difference is 4
There fore nth term is 4n + c [some constant]
Constant can be found by looking at the 'zero' term
First term is 3 therefore zero term is -1 [by ensuring the difference between them is 4]
Nth term is 4n -1
Now make an equation
407 = 4n -1
408 = 4n
102 = n

Therefore there are 102 terms in this sequence

Try the other for your self and see how you get on. I will be around if you need help.
Ciao Gianfranco

Answer 3

Now, for the second ap.

2,9,16,...................., 709

d = 7; a = 2; n= ?

709 = 2 + (n-1) 7
=> n = 102

Answer 4

Now what to do ?

Answer 5

both are arithmetic progressions.
2,9,16....709
\[first term,t_1=2 \space \space \space \space last term, t_n=709\]
common difference= difference between any 2 consecutive terms.\[t_2-t_1=9-2=7\]
\[no\space of \space terms\space \space ,n =\frac {(t_n-t_1)}{d} +1\]
here,
\[n=\frac{709-2}{7} +1=\frac{707}{7} +1=101+1=102\]

Answer 6

I have calculated the no. of terms in both case and it is 102

Answer 7

Now what to do I have to calculate the number of common terms in both ap.

Answer 8

Hmm, the first set of terms are of form 7k +2 and the second set are 4k +3, is that right?

Answer 9

When does 4k+3 = 7k +2?

k= 1/3 not an integer, so no common terms.

Answer 10

Ok thanks for help estudier