The number of common terms in the two
sequences 17,21,25,….,417 and 16,21,26,….466 is

(1)78 (2) 19 (3)20 (4)77 (5) 22

Solution follows here:

__Solution:__
Both
the given series’ are in A.P.

Number
of terms in the 1

^{st}series: 417 = 17+(n_{1}-1)4 => n_{1}-1 = 400/4 = 100 => n_{1}=101
Number
of terms in the 2

^{nd}series: 466 = 16+(n_{2}-1)5 => n_{2}-1 = 450/5 = 90 => n_{2}=91
To
find number of common terms:

Let
m’th term of the first sequence = n’th term of the second sequence

Using
formula for n’th term in an AP with initial term ‘a’ and common difference ‘d’,

t

_{n}= a+(n-1)d,
17+(m-1)4
= 16+(n-1)5 => 4m-4+17 = 5n-5+16 => 4m+2 = 5n

=>
we can observe that, m’th term of the first sequence is equal to the n’th term of
the second sequence, for

m=2, n=2;

m=7,
n=6;

m=12,
n=10;

…
and so on…

m=97,
n=78;

2

^{nd}, 7^{th}, 12^{th}, …..97^{th}terms of the first series are respectively equal to the 2^{nd}, 6^{th}, 10^{th}, …..78^{th}terms of the second series. These are the common terms.
Number of common terms: 97 = 2+(x-1)5 => x-1
= 95/5 = 19=> x=20

**Answer (3)**
wrong ans..right ans is 77

ReplyDeleteThank you for the approach

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