Question

seventh term of an A.p is 5 times it's 1st term and common difference is 2 then find the 1st term​

Answer 1

$\sf\huge\blue{\underline{\underline{ Question : }}}$

Seventh term of an AP is 5 times it's first term and the common difference (d) is 2.Then find first term.

$\sf\huge\blue{\underline{\underline{ Solution: }}}$

★ Given that,

• Seventh term of AP is 5 times if it's first term.
• $\tt\green{ a_{7} = 5a ....(1)}$
• Common difference (d) = 2

★ Let,

$\rm\:\implies a + 6d = 5a$

$\rm\:\implies 5a - a - 6d = 0$

$\rm\:\implies 4a - 6d = 0$

• Substitute the value of d.

$\rm\:\implies 4a - 6(-2) = 0$

$\rm\:\implies 4a + 12 = 0$

$\rm\:\implies 4a = 0 - 12$

$\rm\:\implies 4a = - 12$

$\rm\:\implies a = \frac{- 12}{4}$

$\rm\:\implies a = - 3$

★ Verification,

• Substitute the values of a & d in (1)

$\rm\:\implies -3 - 6(2) = 5(-3)$

$\rm\:\implies -3 - 12 = - 15$

$\rm\:\implies - 15 = - 15$

Hence, LHS = RHS. It was verified.

$\underline{\boxed{\bf{\purple{ \therefore First\:term\:(a) = - 3}}}}\:\orange{\bigstar}$

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★ Important formulas in AP :

$\bf\red{\implies a_{n} = a + (n - 1)d }$

$\bf\red{\implies S_{n} = \frac{n}{2} [ 2a + (n - 1)d ] }$

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