Question

The sum of the 4th and 8th term of an ap is 24 and the sum of the 6th and 10th term of an ap is 44 find the first three term of the ap

Answer 1

Answer:

a+3d+a+7d=24

2a+10d=24

a+5d+a+9d=44

2a+14d=44

from these two equation,on sub

4d=20

d=5

then,2a=24-50

a=-13

then the first three terms of a.p are -13,-13+5,-13+2*5

so,-13,-8,-3

Answer 2

$\large\underline{Given:-}$

• Sum of 4th term and 8th term ⇢ 24
• Sum of 6th term and 10th term ⇢ 44

$\large\underline{To find:-}$

• find the first three terms of the Ap.

$\large\underline{Solutions:-}$

• $\: \: \: \: \: {a_4} \: + \: {a_8} \: \: = \: \: {24}$
• $\: \: \: \: \: {a_6} \: + \: {a_{10}} \: \: = \: \: {44}$

$\: \: \: \: \: {a_4} \: + \: {a_8} \: \: = \: \: {24}$

$\: \: \: \: \: {a} \: + \: {3d} \: + {a} \: + \: {7d} \: \: = \: \: {24}$

$\: \: \: \: \: {2a} \: + \: {10d} \: \: = \: \: {24}$

»★ Divide both side by 2.

$\: \: \: \: \: {a} \: + \: {5d} \: \: = \: \: {12} \: \: \: \: \: .....{(1)}.$

And,

$\: \: \: \: \: {a_6} \: + \: {a_{10}} \: \: = \: \: {44}$

$\: \: \: \: \: {a} \: + \: {5d} \: + {a} \: + \: {9d} \: \: = \: \: {44}$

$\: \: \: \: \: {2a} \: + \: {14d} \: \: = \: \: {44}$

»★ Divide both side by 2.

$\: \: \: \: \: {a} \: + \: {7d} \: \: = \: \: {22} \: \: \: \: \: .....{(2)}.$

✰ Subtracting Eq. (1) and Eq. (2), We get.

${a} \: + \: {5d} \: \: = \: \: {12} \\ {a} \: + \: {7d} \: \: = \: \: {22} \\ \underline{- \: \: \: \: - \: \: \: \: = \: \: - \: \: \: \: } \\ \: \: \: \: \: \: \: \: {2d} \: \: \: \: = \: \: \: {10}$

$\: \: \: \: \: \leadsto {d} \: \: = \: \: \frac{10}{2}$

$\: \: \: \: \: \leadsto {d} \: \: = \: \: {5}$

✰ Then, Putting the value of d in Eq. (1)

$\: \: \: \: \: \leadsto {a} \: + \: {5d} \: \: = \: \: {12}$

$\: \: \: \: \: \leadsto {a} \: + \: {5} \: \times \: {5} \: \: = \: \: {12}$

$\: \: \: \: \: \leadsto {a} \: + \: {25} \: \: = \: \: {12}$

$\: \: \: \: \: \leadsto {a} \: \: = \: \: {12} \: - \: {25}$

$\: \: \: \: \: \leadsto {a} \: \: = \: \: {-13}$

»★ Now, first three terms of Ap are a, a + d, and a + 2d.

$\: \: \: \: \: \leadsto {a} \: \: = \: \: {-13}$

$\: \: \: \: \: \leadsto {a} \: + \: {d}\: \: = \: \: {-13} \: + \: {5} \: \: = \: \: {-8}$

$\: \: \: \: \: \leadsto {a} \: + \: {2d}\: \: = \: \: {-13} \: + \: {2} \: \times \: {5} \: \: = \: \: {-13} \: + \: {10} \: \: = \: \: {-3}$

»★Hence,

first three terms of Ap is -13, -8 And -3.

______________________________________