Math, asked by mani202002, 1 year ago

find the 31st term of AP whose 11th term is 38 and 16th term is 73

Answers

Answered by TooFree

an = a1 + (n - 1)d

when n = 11 ( 11 term):

38 = a1 + ( 11 - 1) d

38 = a1 + 10d ---------------------------- [ 1 ]

When n = 16 ( 16th term):

73 = a1 + ( 16 - 1) d

73 = a1 + 15d ---------------------------- [ 2 ]

Find d:

[ 2 ] - [ 1 ]:

5d = 35

d = 35 ÷ 5 = 7 ---------------------------- Sub into [ 1 ]

Find a:

38 = a1 + 10d

38 = a1 + 10 (7)

38 = a1 + 70

a1 = -32

Find the AP:

an = -32 + (n - 1)(7)

an = -32 + 7n - 7

an = 7n - 39

Find the 31st term:

an = 7n - 39

an = 7(31) - 39 = 178

Answer: The 31st term is 178.

mani202002: find d: [2] - [1] 5d=35 how 5d=35

PADMINI: means you should subtract 1st equation from 2nd equation . 15d - 10d = 5d . and 73 - 38 = 35

Anonymous: Yep!!!

mani202002: ok

Answered by Anonymous

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$We know that formula of AP Tn=a+(n-1)d$

$ Given 11th term then $

$T11=a+10d=)38[Equation (a)$

$T16=a+15d=)73[Equation (b) $

$NOW Solving the Equation $

$a+10d=38 $
$a+15d=73 $
______________________
$-5d=-35 $
$d=35/5=7 $

$Now putting the value of d in Equation (a) $
$ a+10(7)=38 $

$a+70=38 $

$a=38-70=-32 $

$Again $

$ACCORDING TO THE QUESTION $

$Solving Ist Terms $
$Tn=a+(n-1)d $

$Tn=-32+(31-1)7 $
$Tn=-32+(30)7 $
$Tn=-32+210 $
$Tn=178 $

$Thanks!!!!! $

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