The 8th common term of the series S1 = 3 + 7 + 11 + 15 + 19 +, S2 = 1 + 6 + 11 + 16 + 21 +, is

The 8th common term of the series S1 = 3 + 7 + 11 + 15 + 19 +, S2… — Solution | JEE Mathematics

NVAMediumJEE 2023Arithmetic Progression (AP)

The ** $8$ **th common term of the series $S_1 = 3 + 7 + 11 + 15 + 19 + \dots$ , $S_2 = 1 + 6 + 11 + 16 + 21 + \dots$ , is _____

Correct answer:151

Standard Method

Given: The series are $S_1 = 3 + 7 + 11 + 15 + 19 + \dots$ and $S_2 = 1 + 6 + 11 + 16 + 21 + \dots$ .

Find: The ** $8$ **th common term.

From the solution, the common terms form an AP starting with $11$ and common difference $20$ .

Using the nth term formula of an AP:

T_8 = 11 + (8 - 1) \times 20

So,

= 11 + 140 = 151

Therefore, the ** $8$ **th common term is $151$ .

Using the common difference of either original AP, namely $4$ or $5$ , for the common-term AP. This is wrong because the sequence of common terms is a different AP. First identify common terms, then use its own common difference.
Treating $11$ as the first term of one original series instead of the first common term. This is wrong because the question asks about common terms only. Start the AP of common terms from $11$ .
Substituting incorrectly in $a_n = a + (n-1)d$ by using $n$ instead of $n-1$ . This shifts the term number and gives the wrong result. Use $8-1$ for the ** $8$ **th term.

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