The common difference of the A.P. a 1 , a 2 , … , a m i s 13 more than the common difference of the A.P. b 1 , b 2 , … , b n . If b 31 = - 277 , b 43 = - 385 a n d a 78 = 327 , then a 1 is equal to [2026]

Question

The common difference of the A.P. $a_{1}, a_{2}, \dots, a_{m} is 13$ more than the common difference of the A.P. $b_{1}, b_{2}, \dots, b_{n}$ . If $b_{31} = - 277, b_{43} = - 385 and a_{78} = 327$ , then $a_{1}$ is equal to [2026]

Smart Achievers · Accepted Answer

(4)

$Let common difference of A.P.'s are d_{1} & d_{2}$

$∴$ $d_{1} = 13 + d_{2}$

$b_{1} + 30 d_{2} = - 277 . . . (1)$

$b_{1} + 42 d_{2} = - 385 . . . (2)$

$By (2) - (1)$

$12 d_{2} = - 108$

$d_{2} = - 9$

$∴$ $d_{1} = 4$

$Now a_{78} = 327$

$\Rightarrow a_{1} + 77 d_{1} = 327$

$\Rightarrow a_{1} + 308 = 327$

$a_{1} = 19$

Solution

Q.
The common difference of the A.P. $a_{1}, a_{2}, \dots, a_{m} is 13$ more than the common difference of the A.P. $b_{1}, b_{2}, \dots, b_{n}$ . If $b_{31} = - 277, b_{43} = - 385 and a_{78} = 327$ , then $a_{1}$ is equal to [2026]

1 21

2 16

3 24

4 19

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