Question

the sum of the 3rd and 5th terms of an ap is 16and the sum of the 7th and 12th terms is 38 find the first four terms​

Answer 1

Answer:

the sum of the 3rd and 5th terms of an ap is 16

a+2d+ a+4d= 16

2a+ 6d= 16....¹

the sum of the 7th and 12th terms is 38

a+6d+ a+11d= 38

2a+17d= 38...²

form 1 and 2

-11d=-22

d=2

put d in 1

2a+12=16

2a=4

a=2

the first four terms

2,4,6,8

Answer 2

$\huge{\mathtt{\purple{A}\green{n}\pink{s}\blue{w}\purple{E}\red{r}\pink{!}\blue{!}}}$

$\sf\large\underline\pink{Given:-}$

$\sf\a\:_3 + a\:_5=16$

$\sf{\implies a + 2d + a + 4d = 16}$

$\sf{\implies 2a + 6d = 16}$

$\sf{\implies a + 3d = 8}$ _________(i)

_________________________

$\sf\a \:_7 + a \:_12 = 38$

$\sf{\implies a + 6d + a + 11d = 38}$

$\sf{\implies 2a + 17d = 38}$ ________(ii)

$(i) \times 2 - (ii) \times 1$

$\sf\{\implies 2a + 6d - 2a - 17d = 16 - 38}$

$\sf\{\implies -11d = -22}$

$\sf\{\implies d = 2}$

тнєяєƒσяє, α = 8 - 3∂ (ƒяσм i)

= 8 -3×2

= 8 - 6

= 2

тнє ƒirѕт ƒσυя тєямѕ αяє :- 2 , 4, 6, 8