Question

5. If 7th and 13th terms of 2 points
an A.P be 34 and 64
respectively, then its 18th
térm is *
O 87
88
89
90द सम ऑफ फर्स्ट 10 नेचुरल नंबर इज ​

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large\underline{\green{\bf Given :-}}$

$\:\:$

• 7th term of AP is 34

$\:\:$

• 13th term of AP is 64

$\:\:$

$\large\underline{\red{\bf To \: Find :-}}$

$\:\:$

• 18th term

$\:\:$

$\large\underline{\orange{\bf Solution :-}}$

$\:\:$

We know that ,

$\:\:$

➠ $\sf a_n = a + (n - 1)d$ ⚊⚊⚊⚊ ⓵

$\:\:$

Where,

$\:\:$

• $\sf a_n$ = nth term

• a = First term

• n = Number of terms

• d = Common difference

$\:\:$

$\underline{\bold{\texttt{For 7th term :}}}$

$\:\:$

• $\sf a_n$ = 34

• a = a

• n = 7

• d = d

$\:\:$

⟮ Putting these values in ⓵ ⟯

$\:\:$

➜ $\sf a_n = a + (n - 1)d$

$\:\:$

➜ $\sf 34 = a + (7 - 1)d$

$\:\:$

➜ 34 = a + 6d ⚊⚊⚊⚊ ⓶

$\:\:$

$\underline{\bold{\texttt{For 13th term :}}}$

$\:\:$

• $\sf a_n$ = 64

• a = a

• n = 13

• d = d

$\:\:$

⟮ Putting these values in ⓵ ⟯

$\:\:$

➜ $\sf a_n = a + (n - 1)d$

$\:\:$

➜ $\sf 64 = a + (13 - 1)d$

$\:\:$

➜ 64 = a + 12d ⚊⚊⚊⚊ ⓷

$\:\:$

{ Subtracting equation ⓶ from ⓷ ⟯

$\:\:$

➜ 64 - 34 = a + 12d - a - 6d

$\:\:$

➜ 30 = 6d

$\:\:$

➨ d = 5 ⚊⚊⚊⚊ ⓸

$\:\:$

• Hence the Common difference is 5

$\:\:$

⟮ Putting d = 5 from ⓸ to ⓶ ⟯

$\:\:$

➜ 34 = a + 6d

$\:\:$

➜ 34 = a + 6(5)

$\:\:$

➜ 34 = a + 30

$\:\:$

➜ a = 34 - 30

$\:\:$

➨ a = 4 ⚊⚊⚊⚊ ⓹

$\:\:$

• Hence the first term is 4

$\:\:$

$\underline{\bold{\texttt{For 18th term :}}}$

$\:\:$

• $\sf a_n = a_{18 }$

• a = 4

• n = 18

• d = 5

$\:\:$

⟮ Putting these values in ⓵ ⟯

$\:\:$

➜ $\sf a_n = a + (n - 1)d$

$\:\:$

➜ $\sf a_{ 18 } = 4 + (18 - 1)5$

$\:\:$

➜ $\sf a_{ 18 } = 4 + 17(5)$

$\:\:$

➜ $\sf a_{ 18 } = 4 + 85$

$\:\:$

➨ $\sf a_{ 18 } = 89$

$\:\:$

• Hence the 18th term of given AP is 89

$\:\:$

═════════════════════════