The 8 t h common term of the series S 1 = 3 + 7 + 11 + 15 + 19 + . . . , S 2 = 1 + 6 + 11 + 16 + 21 + . . . . . is _________ . [2023]

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Solution

Q.
The $8^{t h}$ common term of the series

$S_{1} = 3 + 7 + 11 + 15 + 19 + . . .,$

$S_{2} = 1 + 6 + 11 + 16 + 21 + . . . . .$

is _________ . [2023]

Ans.
(151)

$S_{1} = 3 + 7 + 11 + 15 + 19 + \dots$

$a_{1} = 3, d_{1} = 4$

$S_{2} = 1 + 6 + 11 + 16 + 21 + \dots$

$a_{2} = 1, d_{2} = 5$

First common term, $a$ = 11

$Common difference, d = LCM (d_{1}, d_{2}) = LCM (4, 5) = 20$

$8^{t h}$ common term of the series

$a_{8} = a + 7 d = 11 + 7 \times 20 = 151$

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