Question

if 6th term of an ap is -10 and its 10th term is - 26 then find the 15th term of an ap

Answer 1

hey

here is ur answer

Answer 2

$\large\underline{Given:-}$

• 6th term of an Ap ⇢ -10
• 10th term of that Ap ⇢ -26

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

• find it's 15th term...?

$\large\underline{Solutions:-}$

$\: \: \: \: \: \star \: \: \: {a_n} \: \: = \: \: {a} \: + \: {(n \: - \: {1})} \: d$

• a ⇢ first term
• d ⇢ common difference
• n ⇢ number of term
• an ⇢ last term

»★ We have

✰ 6th term of an Ap ⇢ -10

$\: \: \: \: \: \leadsto \: \: {a} \: + \: {({6} \: - \: {1})} \: d \: \: = \: \: {-10}$

$\: \: \: \: \: \leadsto \: \: {a} \: + \: {5d} \: \: = \: \: {-10} \: \: \: \: \: \: \: ....{(i)}.$

✰ And, 10th term of that Ap ⇢ -26

$\: \: \: \: \: \leadsto \: \: {a} \: + \: {({10} \: - \: {1})} \: d \: \: = \: \: {-26}$

$\: \: \: \: \: \leadsto \: \: {a} \: + \: {9d} \: \: = \: \: {-26} \: \: \: \: \: \: \: ....{(ii)}.$

»★ Now, Subtracting Eq. (i) and Eq. (ii)

${a} \: + \: {5d} \: \: = \: \: {-10} \\ {a} \: + \: {9d} \: \: = \: \: {-26} \\ \underline{- \: \: \: \: \: \: \: - \: \: \: \: = \: \: \: \: + \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \: \: \: \: \: \: \: \: {-4d} \: \: \: \: \: = \: \: \: {16}$

$\: \: \: \: \: \leadsto \: \: d \: \: = \: \: \frac{-16}{4}$

$\: \: \: \: \: \leadsto \: \: {-4}$

»★ Now, putting the value of d in Eq. (i)

$\: \: \: \: \: \leadsto \: \: {a} \: + \: {5d} \: \: = \: \: {-10}$

$\: \: \: \: \: \leadsto \: \: {a} \: + \: {5} \: \times \: {-4} \: \: = \: \: {-10}$

$\: \: \: \: \: \leadsto \: \: {a} \: - \: {20} \: \: = \: \: {-10}$

$\: \: \: \: \: \leadsto \: \: {a} \: \: = \: \: {-10} \: + \: {20}$

$\: \: \: \: \: \leadsto \: \: {a} \: \: = \: \: {10}$

✰ Let the 15th term be a + 14d

Then, by putting the value of a and d.

$\: \: \: \: \: \leadsto \:\: {a_{15}} \: \: = \: \: {a} \: + \: {14d}$

$\: \: \: \: \: \leadsto \: \: {a_{15}} \: \: = \: \: {10} \: + \: {14} \: \times \: {-4}$

$\: \: \: \: \: \leadsto \:\: {a_{15}} \: \: = \: \: {10} \: - \: {56}$

$\: \: \: \: \: \leadsto {a_{15}} \: \: = \: \: {-46}$

$\: \: \: \: \: \star \: \: \: Hence,$

$\: \: \: \: \: \therefore {15th} \: \: term \: \: is \: \: {-46}$

$\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star\star$