Question

Find the A.P whose 10th term is 5 and 18th term is 77​

Answer 1

Step-by-step explanation:

T10 = a+(n-1) d

5 = a +9d......(1)

T18 = a +(n-1)d

77 = a +17d.......(2)

(2) - (1)=>

77 = a +17d

5 = a +9d

_____________

72 = 8d

d = 9

Now,

5 = a +9×9

a = 5 - 81

a = (-76)

So, your A.P will be,

(A-D),A,(A+D),

-85,-76,-67

Hope it helps uh!

Answer 2

Answer:

${\pink{\green{\sf{\therefore A.P=-76,-67,-58,.......}}}}$

Step-by-step explanation:

$\huge{\pink{\green{\underline{\red{\sf{SOLUTION-}}}}}}$

▪In this question information about two terms .

▪So,from those two terms we find first term and common difference .

▪We have to find A.P.

$\underline\bold{given : } \\ \implies a_{10} = 5 \\ \implies a_{18} =77 \\ \\ \underline\bold{to \: find : } \\ \implies A.P= ?$

▪According to given question :

$\implies a_{10} = 5 \\ \implies a + 9d = 5 - - - - - (1) \\ \\ \implies a_{18} = 77 \\ \implies a + 17d = 77 - - - - - (2) \\ \\ subtracting \: (1) \: from \: (2) \\ \implies a + 17d - (a + 9d) = 77 - 5 \\ \implies a + 17d - a - 9d = 72 \\ \implies 8d = 72 \\ \bold{\implies d = 9 } \\ \\ putting \: value \: of \: d \: in \: (1) \\ \implies a + 9d = 5 \\ \implies a + 9 \times 9 = 5 \\ \implies a = 5 - 81 \\ \bold{\implies a = - 76} \\ \\ \bold{ \implies A.P= - 76,- 67,- 58......}$

_________________________________________