Which term of the AP: -2, -7, -12,... will be -77? Find the sum of this AP up to the term -77

Solution:

Given, the series is -2, -7, -12,......., -77.

We have to find the sum up to the term -77.

From the series,

First term, a = -2

Last term, l = -77

Common difference, d = -7 - (-2) = -7 + 2 = -5

The nth term of the series in AP is given by

aₙ = a + (n - 1)d

So, -77 = -2 + (n - 1)(-5)

-77 + 2 = (n - 1)(-5)

75 = (n - 1)(5)

n - 1 = 75/5

n - 1 = 15

n = 15 + 1

n = 16

If l is the last term of an AP, then the sum of the terms is given by

S = n/2[a+l]

So, S = 16/2[-2 + (-77)]

S = 8[-2 - 77]

= 8(-79)

S = -632

Therefore, the sum of the term is -632.

✦ Try This: Which term of the AP: 2, 6, 10,... will be 46? Find the sum of this AP up to the term 46

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5

---

NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 22

Which term of the AP: -2, -7, -12,... will be -77? Find the sum of this AP up to the term -77

Summary:

The 18th term of the AP: -2, -7, -12,... will be -77. The sum of this AP up to the term -77 is -632

---

☛ Related Questions:

• In an AP, if Sₙ = 3n² + 5n and ak = 164, find the value of k
• If Sₙ denotes the sum of first n terms of an AP, prove that S₁₂ = 3(S₈ - S₄)
• Find the sum of first 17 terms of an AP whose 4th and 9th terms are -15 and -30 respectively