Question

If the sum of n terms of an AP is 5n^2+2n, then find its 19th term​

Answer 1

Answer:

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Step-by-step explanation:

There is a simple trick to finding the nth term of a series whose sum upto n terms is given.

There is a simple trick to finding the nth term of a series whose sum upto n terms is given.nth term = (sum of n terms) - (sum of n-1 terms)

There is a simple trick to finding the nth term of a series whose sum upto n terms is given.nth term = (sum of n terms) - (sum of n-1 terms)According to the given formula, Sum of n terms is 5n^2 + 2n and that of n-1 terms is 5(n-1)^2 + 2(n-1)

There is a simple trick to finding the nth term of a series whose sum upto n terms is given.nth term = (sum of n terms) - (sum of n-1 terms)According to the given formula, Sum of n terms is 5n^2 + 2n and that of n-1 terms is 5(n-1)^2 + 2(n-1)Thus, nth term = 5[n^2-(n-1)^2] + 2[n-(n-1)]

There is a simple trick to finding the nth term of a series whose sum upto n terms is given.nth term = (sum of n terms) - (sum of n-1 terms)According to the given formula, Sum of n terms is 5n^2 + 2n and that of n-1 terms is 5(n-1)^2 + 2(n-1)Thus, nth term = 5[n^2-(n-1)^2] + 2[n-(n-1)]= 5[(n+n-1)(n-(n-1))] + 2(1)

There is a simple trick to finding the nth term of a series whose sum upto n terms is given.nth term = (sum of n terms) - (sum of n-1 terms)According to the given formula, Sum of n terms is 5n^2 + 2n and that of n-1 terms is 5(n-1)^2 + 2(n-1)Thus, nth term = 5[n^2-(n-1)^2] + 2[n-(n-1)]= 5[(n+n-1)(n-(n-1))] + 2(1)= 5(2n-1)(1) + 2

There is a simple trick to finding the nth term of a series whose sum upto n terms is given.nth term = (sum of n terms) - (sum of n-1 terms)According to the given formula, Sum of n terms is 5n^2 + 2n and that of n-1 terms is 5(n-1)^2 + 2(n-1)Thus, nth term = 5[n^2-(n-1)^2] + 2[n-(n-1)]= 5[(n+n-1)(n-(n-1))] + 2(1)= 5(2n-1)(1) + 2= 10n-3

Answer 2

Answer:

187

Step-by-step explanation:

Sum = $\frac{n}{2}(2a_{1} + (n-1)d$)

$\frac{n^2}{2}d-\frac{n}{2}d +a_{1} n$ = 5n² + 2n

n²d/2 = 5n² ⇒ d = 10

n( - d/2 + a) = 2n

- 10/2 + a = 2 ⇒ a = - 7

$a_{n} = a_{1} + (n - 1)d$

$a_{19} = 7 + (19 - 1)(10)$ = 187