Question

The 10th term of an ap is -4 and the 22nd term is -16 .find its 38 term

Answer 1

EXPLANATION.

• GIVEN

10th term of an Ap = -4

22nd term of an Ap = -16

find it's 38 term,

according to the questions,

T10 = a + 9d = -4 .....(1)

T22 = a + 21d = -16 ......(2)

From equation (1) and (2) we get,

-12d = 12

d = -1

put the value of d = -1 in equation (1)

we get,

a + 9(-1) = -4

a - 9 = -4

a = -4 + 9

a = 5

to find 38th term,

a + 37d

5 + 37(-1)

-32

Therefore,

38th term of Ap = -32

Answer 2

$\huge \underline{ \blue{ \boxed{ \bf \red{Answer:-}}}}$

$\purple{\bold{\underline{\underline{Given:-}}}}$

• 10th Term = –4

• 22nd Term = –16

$\blue{\bold{\underline{\underline{To \: Find:-}}}}$

• 38th Term

$\bf \underline{ \orange{ \boxed{ \bf \green{Formula \: Used:}}}}$

$a _{n} = a + (n - 1)d$

Where n = 10 , 22 , 38

$a _{10} = a + 9d$

$a _{22} = a + 21d$

10th Term = –4

$a + 9d = - 4 \: \: \: \: \: ...(i)$

22nd Term = –16

$a + 21d = - 16 \: \: \: \: ...(ii)$

We found ( i ) and ( ii ) :

$- 12d = 12$

$d = - 1$

Now, Putting the value of d in equation ( i ) :

$a +(9 \times ( - 1) )= - 4$

$a = 5$

Now, 38th Term

$a_{38} = a + 37d$

Put The Values :

$a_{38} = 5+ 37 \times( - 1)$

$a _{38} = - 32$

Hence 38th Term = –32.

$\bf\blue{Hope\ it\ helps.}$

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