Question

Which term of the ap -2, -7, -12.... will be -77? How to find the sum of this ap upto the term -77?

Answer 1

$\large{\underline{\bf{\pink{Answer:-}}}}$

✰ 16th term of AP will be -77

✰ sum of 16th terms is -632

$\large{\underline{\bf{\blue{Explanation:-}}}}$

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

✰ Given ap = -2,-7,-12.......

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

✰ we need to find that term of AP that will be -77.

$\huge{\underline{\bf{\red{Solution:-}}}}$

✰ a = -2

✰ d = -7-(-2) = -5

✰ an = -77

$\bf\pink{an=a+(n-1)d}$

$:\implies$ -77= -2+(n - 1)-5

$:\implies$ -77 +2 = (n- 1)-5

$:\implies$ -75/-5 = n-1

$:\implies$ 15 +1 = n

$:\implies\bf\pink{n=16}$

Now ,

-77 is the 16th term of AP then,

$:\implies\pink{ \:s_n= \frac{n}{2}[2a+(n-1)d}$

$:\implies\:s_n=\frac{16}{2}[2(-2)+(16-1)-5$

$:\implies\:s_n=8[-4+(15)(-5)]$

$:\implies\:s_n=8[-4-75]$

$:\implies\:s_n=8[-79]$

$:\implies\:s_n=-632$

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Answer 2

Step-by-step explanation:

Given -

A•P = -2, -7, -12, .......... -77

To Find -

• Which term of AP will be -77
• How to find sum of this AP upto the term -77

Here,

a = -2

d = -7 - (-2) = -7 + 2 = -5

an = -77

As we know that :-

• an = a + (n - 1)d

→ -77 = -2 + (n - 1)-5

→ -77 + 2 = -5(n - 1)

→ -75/-5 = n - 1

→ 15 = n - 1

→ n = 15 + 1

→ n = 16

And

As we know that :-

• sn = n/2[2a + (n - 1)d]

→ 16/2[2(-2) + (16-1)-5]

→ 8 [-4 - 75]

→ 8 × -79

→ -632

Hence,

The 16th term of the AP is -77

And

The sum of this AP upto the term -77 is -632.