Question

the first term of an ap is 17 and last term of an ap is 360 respectively. if the common difference is 9 . how many terms are there and what are there sum
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Answer 1

★ Correct Question:

The first term of an AP is 17 and last term of an ap is 350 respectively. If the common difference is 9 . how many terms are there and what are there sum

★ Given:-

• First term = a = 17

• Last term = aₙ = 350

• Common difference = d = 9

★To find:-

➳ Number of terms = n = ?

➳ Sₙ = ?

★Formulas used:-

$\large{ \red{ \star}} \: \sf{S _{n} = \dfrac{n}{2} \times (a + a _{n})} \\ \\ \large{ \red{ \star}} \: \sf{a _{n} = a + (n - 1)d}$

★Method:-

Applying the above formula,

aₙ = a + (n - 1)d

→ 350 = 17 + (n - 1)9

→ 350 = 17 + 9n - 9

→ 350 = 8 + 9n

→ 350 - 8 = 9n

→ 342 = 9n

∴ n = 38

So, there are 38 terms in the A.P

⛇ Now let's find the sum.

$\sf{S _{n} = \dfrac{n}{2} \times (a + a _{n} )}$

$\implies \sf{S _{n} = \dfrac{38}{2} \times (17 + 350)} \\ \\ \implies \sf{S _{n} = 19(367)} \\ \\ \implies \boxed{ \boxed{ \bf{S _{n} = 6973}}}$

∴ Sum of n terms = 6973