Question

Q]In an A.P a7 and a5 are 46 and 12.

[a] Find common difference
[b] Find first term
[c] find a20 term
[d] find nth term of this A.P​

Answer 1

Step-by-step explanation:

a7 = 46

a5 = 12

a+6d = 46..... (1)

a+4d = 12...... (2)

solve 1st nd 2nd by elimination method

2d = 34

d = 17. (common difference )

put d = 17

a+4×17 = 12

a+68 =12

a= 12 -68

a= - 56 ( first term)

To find a20

a+19d

-56+19 ×17

a20 = -56 + 323

a20 = 267

To find nth term

a+(n-1)d

-56 + (n-1) 17=0

-56+17n -17 =0

17n = 73

n = 73/17

Answer 2

Answer:

${\bold{\therefore (a)=Common\:difference=17}}$

${\bold{\therefore (b)=First\:term=-56}}$

${\bold{\therefore (c)=a_{20}=257}}$

${\bold{\therefore (d)=nth\:term=17n-73}}$

Step-by-step explanation:

${\bold{\huge{\underline{SOLUTION-}}}}$

• In the given question information given about two known terms of an A.P.

• We have to find common difference, first term, a20th term and nth term.

$\underline \bold{Given : } \\ \implies a_{7} = 46 \\ \implies a_{5} = 12 \\ \\ \underline \bold{To \: Find : } \\ \implies common \: difference(d) = ?\\ \implies first \: term(a) = ?\\ \implies a_{20} =? \\ \implies nth \: term = ?$

• According to given question :

$\bold{For \: a\: part : } \\ \implies a_{7} = 46 \\ \implies a + 6d = 46 - - - - - (1) \\ \\ \implies a_{5} = 12 \\ \implies a + 4d = 12 - - - - - (2) \\ \\ \bold{subtracting \: (2) \: from \: (1) }\\ \implies a + 6d - (a + 4d) = 46 - 12 \\ \implies a + 6d - a - 4d = 34 \\ \implies 2d = 34 \\ \implies d = \frac{34}{2} \\ \bold{\implies d = 17} \\ \\ \bold{For \: b \: part : } \\ \bold{putting \: value \: of \: d \: in \: (1)} \\ \implies a + 6d = 46 \\ \implies a + 6 \times 17 = 46 \\ \implies a + 102 = 46 \\ \implies a = 46 - 102 \\ \bold{\implies a = - 56}$

$\bold{For \: c \: part : } \\ \implies a_{20} = a + 19d \\ \implies a_{20} = - 56 + 19 \times 17 \\ \implies a_{20} = - 56 + 313 \\ \bold{\implies a_{20} =257}$

$\bold{For \: d \: part : } \\ \implies a_{n} =a +( n - 1)d \\ \implies a_{n} = - 56 + (n - 1) \times 17 \\ \implies a_{n} = - 56 + 17n - 17 \\ \bold{\implies a_{n} =17n - 73}$